1932:" for eight of the other themes (all but 1, 5, and 12). Grothendieck wrote that the first and last themes, topological tensor products and regular configurations, were of more modest size than the others. Topological tensor products had played the role of a tool rather than of a source of inspiration for further developments; but he expected that regular configurations could not be exhausted within the lifetime of a mathematician who devoted oneself to it. He believed that the deepest themes were motives, anabelian geometry, and GaloisâTeichmĂŒller theory.
1358:
commonplace and tolerated. The letter also expressed his belief that totally unforeseen events before the end of the century would lead to an unprecedented collapse of civilization. Grothendieck added however that his views were "in no way meant as a criticism of the Royal
Academy's aims in the administration of its funds" and he added, "I regret the inconvenience that my refusal to accept the Crafoord prize may have caused you and the Royal Academy."
735:, given that he had refused to take French nationality (as that would have entailed military service against his convictions). He stayed in SĂŁo Paulo (apart from a lengthy visit in France from October 1953 - March 1954) until the end of 1954. His published work from the time spent in Brazil is still in the theory of topological vector spaces; it is there that he completed his last major work on that topic (on "metric" theory of
1328:('Harvests and Sowings', 1986), Grothendieck describes his approach to mathematics and his experiences in the mathematical community, a community that initially accepted him in an open and welcoming manner, but which he progressively perceived to be governed by competition and status. He complains about what he saw as the "burial" of his work and betrayal by his former students and colleagues after he had left the community.
6303:
6313:
1124:("long-term guest") at the IHĂS, wrote a piece about Grothendieck for a special volume published on the occasion of the IHĂS's fortieth anniversary. In that publication, Cartier notes that as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Grothendieck always had a deep compassion for the poor and the downtrodden. As Cartier puts it, Grothendieck came to find
1430:, claiming that all materials published in his absence had been published without his permission. He asked that none of his work be reproduced in whole or in part and that copies of this work be removed from libraries. He characterized a website devoted to his work as "an abomination". His dictate may have been reversed in 2010.
558:
and worked as a journalist. As teenagers, both of his parents had broken away from their early backgrounds. At the time of his birth, Grothendieck's mother was married to the journalist
Johannes Raddatz and initially, his birth name was recorded as "Alexander Raddatz." That marriage was dissolved in
1108:
while the city was being bombed. In 1966, he had declined to attend the
International Congress of Mathematicians (ICM) in Moscow, where he was to receive the Fields Medal. He retired from scientific life around 1970 after he had found out that IHĂS was partly funded by the military. He returned to
828:
He was so completely unknown to this group and to their professors, came from such a deprived and chaotic background, and was, compared to them, so ignorant at the start of his research career, that his fulgurating ascent to sudden stardom is all the more incredible; quite unique in the history of
1952:
Although mathematics became more and more abstract and general throughout the 20th century, it was
Alexander Grothendieck who was the greatest master of this trend. His unique skill was to eliminate all unnecessary hypotheses and burrow into an area so deeply that its inner patterns on the most
1136:
was heating up, and
Cartier suggests that this also reinforced Grothendieck's distaste at having become a mandarin of the scientific world. In addition, after several years at the IHĂS, Grothendieck seemed to cast about for new intellectual interests. By the late 1960s, he had started to become
1345:
period. The first three volumes (corresponding to Parts 0 to III of the book) were published between 1989 and 1993, while the fourth volume (Part IV) was completed and, although unpublished, copies of it as a typed manuscript are circulated. Grothendieck helped with the translation and wrote a
1357:
with an open letter to the media. He wrote that he and other established mathematicians had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community that was characterized by outright scientific theft that he believed had become
1392:
More than 20,000 pages of
Grothendieck's mathematical and other writings are held at the University of Montpellier and remain unpublished. They have been digitized for preservation and are freely available in open access through the Institut Montpelliérain Alexander Grothendieck portal.
1168:. The group published a bulletin and was dedicated to antimilitary and ecological issues. It also developed strong criticism of the indiscriminate use of science and technology. Grothendieck devoted the next three years to this group and served as the main editor of its bulletin.
777:, but the offer fell through when he refused to sign a pledge promising not to work to overthrow the United States governmentâa refusal which, he was warned, threatened to land him in prison. The prospect of prison did not worry him, so long as he could have access to books.
658:), a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists. Many of the refugee children hidden in Le Chambon attended CollĂšge CĂ©venol, and it was at this school that Grothendieck apparently first became fascinated with mathematics.
44:
1966:
Grothendieck approached algebraic geometry by clarifying the foundations of the field, and by developing mathematical tools intended to prove a number of notable conjectures. Algebraic geometry has traditionally meant the understanding of geometric objects, such as
1401:
In 1991, Grothendieck moved to a new address that he did not share with his previous contacts in the mathematical community. Very few people visited him afterward. Local villagers helped sustain him with a more varied diet after he tried to live on a staple of
508:
and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious pursuits (first
Buddhism and later, a more Catholic Christian vision). In 1991, he moved to the French village of
2364: â Weil cohomology theory for schemes over a base field, whose values are modules over the ring of Witt vectors over the base field, that replaces Zariski open sets by infinitesimal thickenings of Zariski open sets with divided power structures
1975:. In this approach, the properties of a geometric object are related to the properties of an associated ring. The space (e.g., real, complex, or projective) in which the object is defined, is extrinsic to the object, while the ring is intrinsic.
2144:
into the mainstream as an organizing principle for mathematics in general. Among its uses, category theory creates a common language for describing similar structures and techniques seen in many different mathematical systems. His notion of
1644:
with Serre. This result was his first work in algebraic geometry. Grothendieck went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which at the time were in a state of flux and under discussion in
5454:
Kleinert, Werner (2007). "Wer ist
Alexander Grothendieck? Anarchie, Mathematik, SpiritualitÀt. Eine Biographie. Teil 1: Anarchie" [Who is Alexander Grothendieck? Anarchy, mathematics, spirituality. A biography. Part 1: Anarchy.].
1179:
for two years. He then became a professor at the
University of Montpellier, where he became increasingly estranged from the mathematical community. He formally retired in 1988, a few years after having accepted a research position at the
1368:
exists. As part of the notes to this manuscript, Grothendieck described the life and the work of 18 "mutants", people whom he admired as visionaries far ahead of their time and heralding a new age. The only mathematician on his list was
2932:
1990:
is associated to every open subset of the space. Schemes have become the basic objects of study for practitioners of modern algebraic geometry. Their use as a foundation allowed geometry to absorb technical advances from other fields.
1699:
Grothendieck is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation. Relatively little of his work after 1960 was published by the conventional route of the
1927:
Grothendieck wrote that, of these themes, the largest in scope was topoi, as they synthesized algebraic geometry, topology, and arithmetic. The theme that had been most extensively developed was schemes, which were the framework
1414:
located him, then carried on a brief correspondence. Thus they became among "the last members of the mathematical establishment to come into contact with him". After his death, it was revealed that he lived alone in a house in
435:
1704:, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal. His influence spilled over into many other branches of mathematics, for example the contemporary theory of
1544:
in studying linear maps between topological vector spaces. In a few years, he had become a leading authority on this area of functional analysisâto the extent that
Dieudonné compares his impact in this field to that of
1957:
By the 1970s, Grothendieck's work was seen as influential, not only in algebraic geometry and the allied fields of sheaf theory and homological algebra, but influenced logic, in the field of categorical logic.
865:
working groups drafting into foundational work some of the ablest French and other mathematicians of the younger generation). Grothendieck practically ceased publication of papers through the conventional,
1783:. Weil had realized that to prove such a connection, one needed a new cohomology theory, but neither he nor any other expert saw how to accomplish this until such a theory was expressed by Grothendieck.
1377:
who was claimed to have survived on the Holy Eucharist alone, Grothendieck almost starved himself to death in 1988. His growing preoccupation with spiritual matters was also evident in a letter entitled
1340:
in 2025. A partial English translation can be found on the Internet. A Japanese translation of the whole book in four volumes was completed by Tsuji Yuichi (1938â2002), a friend of Grothendieck from the
1192:
While not publishing mathematical research in conventional ways during the 1980s, he produced several influential manuscripts with limited distribution, with both mathematical and biographical content.
2104:
was intended to be the "â-adic" theory but without the choice of "â", a prime number. It did not provide the intended route to the Weil conjectures, but has been behind modern developments in
1775:
that argued for a connection between the topological characteristics of a variety and its diophantine (number theoretic) properties. For example, the number of solutions of an equation over a
1116:
While the issue of military funding was perhaps the most obvious explanation for Grothendieck's departure from the IHĂS, those who knew him say that the causes of the rupture ran more deeply.
1995:
978:
1978:
Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces ("spectra") and associated rings the primary objects of study. To that end, he developed the theory of
1599:. Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory. He shifted attention from the study of individual varieties to his
1496:
during his time in Nancy; three children, Johanna (1959), Alexander (1961), and Mathieu (1965) with his wife Mireille Dufour; and one child with Justine Skalba, with whom he lived in a
1433:
In September 2014, almost totally deaf and blind, he asked a neighbour to buy him a revolver so he could kill himself.On 13 November 2014, aged 86, Grothendieck died in the hospital of
2006:
to their algebraic structure and now bears his name, being called "the GrothendieckâHirzebruchâRiemannâRoch theorem". The tools he developed to prove this theorem started the study of
1953:
abstract level revealed themselvesâand then, like a magician, show how the solution of old problems fell out in straightforward ways now that their real nature had been revealed.
2093:. Grothendieck's large-scale approach has been called a "visionary program". The â-adic cohomology then became a fundamental tool for number theorists, with applications to the
3011:
1171:
Although Grothendieck continued with mathematical enquiries, his standard mathematical career mostly ended when he left the IHĂS. After leaving the IHĂS, Grothendieck became a
2844:
3353:
3778:
5779:
5322:
2481:
1292:
of complex curves. Although Grothendieck never published his work in this area, the proposal inspired other mathematicians to work in the area by becoming the source of
165:
1609:), allowing a broad generalization of many classical theorems. The first major application was the relative version of Serre's theorem showing that the cohomology of a
6382:
4338:
4273:
1708:. Although lauded as "the Einstein of mathematics", his work also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems.
1007:) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time. He went on to introduce the
1728:
999:
655:
6362:
4832:
1676:
has become established as the best universal foundation for this field, because of its expressiveness as well as its technical depth. In that setting one can use
5044:
3246:
1332:
was finally published in 2022 by Gallimard and, thanks to French science historian Alain Herreman, is also available on the Internet. An English translation by
5010:
5784:
5766:
3116:
605:, where his mother contracted the tuberculosis that would eventually cause her death in 1957. While there, Grothendieck managed to attend the local school, at
1738:
1064:
5484:
4954:
4900:
1285:
1181:
488:(IHĂS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He received the
5217:
1971:
and surfaces, through the study of the algebraic equations for those objects. Properties of algebraic equations are in turn studied using the techniques of
6347:
4157:
854:
485:
248:
1748:
5811:
1835:
1629:
1382:
sent to 250 friends in January 1990. In it, he described his encounters with a deity and announced that a "New Age" would commence on 14 October 1996.
833:
His first works on topological vector spaces in 1953 have been successfully applied to physics and computer science, culminating in a relation between
4846:
4973:
4919:
2588:
1650:
1601:
1473:(1954â62). He eventually applied for French citizenship in the early 1980s, after he was well past the age that exempted him from military service.
990:
982:
474:
4256:
2981:
5648:
4040:
2153:. The emergence of a separate mathematical discipline of category theory has been attributed to Grothendieck's influence, although unintentional.
716:. The latter had recently won a Fields Medal. He showed his new student his latest paper; it ended with a list of 14 open questions, relevant for
559:
1929 and Schapiro acknowledged his paternity, but never married Hanka Grothendieck. Grothendieck had a maternal sibling, his half sister Maidi.
1364:, a 315-page manuscript written in 1987, is Grothendieck's account of how his consideration of the source of dreams led him to conclude that a
4074:
1239:
below). Within these, in an informal, diary-like manner, Grothendieck explained and developed his ideas on the relationship between algebraic
5571:
5147:
5114:
4816:
4741:
4682:
4631:
4604:
4570:
4533:
4500:
3543:
2276:
2234:
2014:, which explores the topological properties of objects by associating them with rings. After direct contact with Grothendieck's ideas at the
4205:
1656:
His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions. He adapted the use of non-closed
1469:. Part of his reluctance to hold French nationality is attributed to not wishing to serve in the French military, particularly due to the
632:, although he occasionally had to seek refuge in the woods during Nazi raids, surviving at times without food or water for several days.
3291:
Peixoto, Tatiana; Bietenholza, Wolfgang (2016). "To the Memory of Alexander Grothendieck: a Great and Mysterious Genius of Mathematics".
6387:
601:. He and his mother were then interned in various camps from 1940 to 1942 as "undesirable dangerous foreigners." The first camp was the
4126:
5423:
5393:
5248:
5206:
3004:
2623:
484:
Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the
3211:
Luca Barbieri Viale, 'Alexander Grothendieck:entusiasmo e creativitĂ ,' in C. Bartocci, R. Betti, A. Guerraggio, R. Lucchetti (eds.,)
2853:
957:
Alexander Grothendieck's work during what is described as the "Golden Age" period at the IHĂS established several unifying themes in
4473:
4106:
3918:
3328:
2451:
763:
4257:âHe was in mystic deliriumâ: was this hermit mathematician a forgotten genius whose ideas could transform AI â or a lonely madman?
3958:
1903:
517:, where he lived in seclusion, still working on mathematics and his philosophical and religious thoughts until his death in 2014.
1556:
and related fields where Grothendieck did his most important and influential work. From approximately 1955 he started to work on
5581:
5106:
The Grothendieck Festschrift, Volume I: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck
4410:
3771:
6402:
5330:
5310:
727:, from 1950 to 1953. At this time he was a leading expert in the theory of topological vector spaces. In 1953 he moved to the
5958:
5804:
5080:
5040:
4998:
4984:
4331:
2649:
2198:
2182:
dedicates one chapter to the work and life of Grothendieck, introducing his story by reference to the Japanese mathematician
1117:
783:
691:
5683:: This is an account of how 'Pursuing Stacks' was written in response to a correspondence in English with Ronnie Brown and
4277:
3557:
2221:(1955). "Produits Tensoriels Topologiques et Espaces Nucléaires" [Topological Tensor Products and Nuclear Spaces].
1806:, he identified twelve of his contributions that he believed qualified as "great ideas". In chronological order, they are:
6279:
5771:
5663:
5497:
4562:
4026:
3578:
1255:. The manuscript, which is being edited for publication by G. Maltsiniotis, later led to another of his monumental works,
870:
route. However, he was able to play a dominant role in mathematics for approximately a decade, gathering a strong school.
636:
5161:
4227:
2557:
6377:
6352:
5169:
MatĂ©riaux pour l'histoire des mathĂ©matiques au XXe siĂšcle â Actes du colloque Ă la mĂ©moire de Jean DieudonnĂ© (Nice 1996)
5055:
1828:
1218:
1020:
720:. Grothendieck introduced new mathematical methods that enabled him to solve all of these problems within a few months.
648:
3058:
2409:
6397:
5002:
3399:
2608:
2506:
2101:
1866:
1633:
1573:
922:
662:
338:
3458:
5716:
4987:(1998), "La folle journĂ©e, de Grothendieck Ă Connes et Kontsevich â Ăvolution des notions d'espace et de symĂ©trie",
5948:
5680:
5385:
5226:
2603:
2593:
2573:
1810:
1525:
1280:
1206:
1040:
861:
and Grothendieck. Grothendieck attracted attention by an intense and highly productive activity of seminars there (
728:
677:
where at first he did not perform well, failing such classes as astronomy. Working on his own, he rediscovered the
261:
5529:
1259:. Written in 1991, this latter opus of approximately 2000 pages, further developed the homotopical ideas begun in
6407:
6392:
6372:
6367:
6306:
5797:
5730:
4990:
Les relations entre les mathĂ©matiques et la physique thĂ©orique â Festschrift for the 40th anniversary of the IHĂS
4942:
4888:
4557:
2872:
2628:
2527:
2081:, of the number of points on an algebraic curve or variety of higher dimension. Grothendieck's discovery of the
1945:
1110:
681:. After three years of increasingly independent studies there, he went to continue his studies in Paris in 1948.
674:
597:
In May 1939, Grothendieck was put on a train in Hamburg for France. Shortly afterward his father was interned in
505:
256:
134:
5688:
5674:
2652:
asserts that his mother was of Jewish German descent: "what I know of his life comes from Grothendieck himself".
1999:
1621:
1301:
1141:, a physicist who joined the IHĂS faculty in 1964, said that Grothendieck came to talk to him a few times about
5653:
5553:
5493:
3480:
2522:
2472:
2440:
1529:
1044:
705:
428:
5684:
5003:"A mad day's work: from Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry"
2342:
358:
5539:
2089:
theory, opened the way for a proof of the Weil conjectures, ultimately completed in the 1970s by his student
1940:
Grothendieck is considered by many to be the greatest mathematician of the twentieth century. In an obituary
1617:
of coherent sheaves under a proper map are coherent; this reduces to Serre's theorem over a one-point space.
1389:, published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988.
2613:
2186:. The book is a lightly fictionalized account of the world of scientific inquiry and was a finalist for the
2039:
1438:
834:
6193:
6100:
4946:
4892:
3685:
3150:, p. 2: "Beide beteiligten sich am Spanischen BĂŒrgerkrieg, nicht aktiv kĂ€mpfend, aber unterstĂŒtzend."
3119:[Scientific treasure or unreadable old paper? The mysterious archives of Alexandre Grothendieck].
2361:
2336:
1877:
1016:
640:
99:
3724:
2038:
theories, which use algebraic techniques to study topological objects, has influenced the development of
696:, but he lacked the necessary background to follow the high-powered seminar. On the advice of Cartan and
2973:
2547:
2390:
2352:
2047:
1820:
1537:
1497:
1481:
Grothendieck was very close to his mother, to whom he dedicated his dissertation. She died in 1957 from
1426:
In January 2010, Grothendieck wrote the letter entitled "DĂ©claration d'intention de non-publication" to
1350:
have been translated into Spanish, as well as into a Russian translation that was published in Moscow.
930:
625:
277:
71:
4699:
1757:
1453:. In 1938, aged ten, he moved to France as a refugee. Records of his nationality were destroyed in the
1264:
754:, and increasingly in algebraic geometry. It was in Lawrence that Grothendieck developed his theory of
191:
5774:
5722:
5643:
4646:
R. P. Langlands, Modular forms and l-adic representations, Lecture Notes in Math. 349. (1973), 361â500
2956:
6357:
6342:
6337:
3117:"Trésor scientifique ou vieux papiers illisibles? Les mystérieuses archives d'Alexandre Grothendieck"
2888:
2563:
2435:
2204:
2023:
2011:
1979:
1870:
1847:
1661:
1625:
1211:
1176:
1149:
interested Grothendieck much more than physics, and he organized some seminars on biological topics.
1081:
994:
717:
614:
5639:
5530:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude. Part 3: Spirituality"
4934:
4880:
4134:
2598:
2583:
2467:
2430:
2321:
2187:
2175:
2150:
2125:
2113:
2082:
2078:
2074:
1888:
1857:
1842:
1764:
1689:
1677:
1614:
1561:
1557:
1509:
1416:
1309:
During this period, Grothendieck also gave his consent to publishing some of his drafts for EGA on
1252:
1172:
1008:
906:
751:
724:
701:
589:
as non-combatant auxiliaries. However, others state that Schapiro fought in the anarchist militia.
510:
497:
462:
458:
235:
227:
139:
6312:
5540:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude. Part 2: Mathematics"
4175:
6316:
6269:
6188:
6149:
6132:
6095:
5604:
4826:
3292:
2568:
2414:
2326:
2183:
2137:
2109:
2105:
2063:
2055:
2043:
2015:
2007:
1909:
1899:
1693:
1553:
1458:
1310:
1297:
1272:
1244:
958:
890:
770:
755:
747:
547:
493:
454:
363:
231:
153:
5279:
5259:
4525:
4387:: " mathematician of staggering accomplishment... a legendary figure in the mathematical world."
4201:
1293:
1043:
and he then conjectured the existence a further generalization of it, which is now known as the
5067:
3193:
Piotr Pragacz, 'Notes on the Life and Work of Alexander Grothendieck,' in Piotr Pragacz (ed.),
570:. His mother followed soon thereafter. Grothendieck was left in the care of Wilhelm Heydorn, a
6230:
6203:
6198:
6144:
6117:
6063:
5997:
5904:
5875:
5735:
5567:
5547:
5509:
5501:
5429:
5419:
5389:
5244:
5238:
5202:
5143:
5124:
5110:
4812:
4737:
4731:
4678:
4627:
4621:
4600:
4594:
4566:
4529:
4496:
4490:
4469:
4457:
4102:
4096:
4055:
3539:
3418:
3273:
3212:
2937:
2914:
2906:
2662:
2282:
2272:
2248:
2230:
2168:
in English), a novel by Puerto RicanâCosta Rican writer Carlos Fonseca is about Grothendieck.
2094:
1983:
1861:
1768:
1592:
1517:
1486:
1222:
1036:
1028:
858:
817:
813:
709:
629:
586:
582:
562:
Grothendieck lived with his parents in Berlin until the end of 1933, when his father moved to
302:
5280:"Comme AppelĂ© du NĂ©ant â As If Summoned from the Void: The Life of Alexandre Grothendieck II"
3230:
3194:
3179:
6284:
6257:
6166:
6127:
6051:
6024:
6002:
5963:
5953:
5870:
5853:
5754:
5596:
5460:
5361:
5260:"Comme AppelĂ© du NĂ©ant â As If Summoned from the Void: The Life of Alexandre Grothendieck I"
5092:
5019:
4963:
4909:
4672:
4552:
3710:
3531:
3408:
3343:
2896:
2852:
2730:
2666:
2618:
2578:
2512:
2492:
2486:
2384:
2316:
2146:
2070:
1987:
1824:
1787:
1646:
1581:
1577:
1521:
1370:
1365:
1153:
1125:
1052:
1048:
1012:
974:
938:
918:
914:
894:
759:
743:
713:
678:
606:
546:
roots and had been imprisoned in Russia before moving to Germany in 1922, while his mother,
478:
388:
318:
297:
289:
5699:
5616:
4580:
4160:[Alexandre Grothendieck, the greatest mathematician of the 20th century, is dead].
3553:
3530:. Lecture Notes in Mathematics. Vol. 1960. New York: Springer-Verlag. pp. 1â259.
3430:
3310:
3308:
2244:
6247:
6220:
6176:
6161:
6041:
5975:
5612:
5464:
5345:
4757:
4576:
4373:
Alexandre Grothendieck is arguably the most important mathematician of the 20th century...
4092:
3660:
3549:
3426:
2541:
2532:
2445:
2424:
2331:
2240:
2193:
2141:
2086:
2003:
1968:
1726:
The bulk of Grothendieck's published work is collected in the monumental, yet incomplete,
1701:
1591:
Homological methods and sheaf theory had already been introduced in algebraic geometry by
1585:
1466:
1450:
1240:
1227:
1101:
970:
874:
867:
842:
801:
732:
543:
539:
470:
445:
348:
328:
75:
5177:
3925:
3849:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai SĆ«gaku-sha.
3830:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai SĆ«gaku-sha.
3811:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai SĆ«gaku-sha.
3809:
The Solitary Adventures of a Mathematician: A Journey into Mathematics and Self-Discovery
3656:
2301:
1565:
5677:, collection of mathematical and biographical information, photos, links to his writings
5443:
4364:
3996:
3951:
2892:
857:(IHĂS), a new privately funded research institute that, in effect, had been created for
6242:
6122:
6073:
6029:
6007:
5992:
5921:
5157:
4988:
4518:
2462:
2419:
2265:
2117:
2090:
2019:
1921:
1791:
1780:
1610:
1354:
1263:. Much of this work anticipated the subsequent development during the mid-1990s of the
1248:
1232:
946:
898:
886:
793:
661:
In 1990, for risking their lives to rescue Jews, the entire village was recognized as "
353:
333:
323:
200:
43:
5741:
5476:
3893:
3605:
673:
After the war, the young Grothendieck studied mathematics in France, initially at the
481:. He is considered by many to be the greatest mathematician of the twentieth century.
17:
6331:
6252:
6225:
6105:
6090:
6078:
6068:
6046:
5980:
5936:
5841:
5726:
5534:
Third part of planned four-volume biography; crowd-financed translation into English.
4938:
4930:
4884:
4876:
4461:
4425:
4327:
3516:
2868:
2670:
2517:
2497:
2370:
1941:
1924:
writes the other terms "Ariadne's thread" and "philosophy" as effective equivalents.
1893:
1814:
1772:
1685:
1681:
1669:
1657:
1546:
1533:
1513:
1462:
1407:
1333:
1204:) is a 1600-page handwritten manuscript containing many of the ideas that led to the
1157:
1093:
1032:
962:
934:
902:
821:
809:
789:
774:
746:
at the beginning of 1955, and there he set his old subject aside in order to work in
697:
602:
450:
157:
117:
5748:
5299:
3348:
6019:
5858:
5836:
5820:
5375:
5219:
Récoltes et Semailles : réflexions et témoignage sur un passé de mathématicien
5195:
Récoltes et Semailles : réflexions et témoignage sur un passé de mathématicien
4260:
2475: â cohomology theory for algebraic varieties introduced by Grothendieck (1966)
2311:
2051:
1776:
1641:
1613:
on a complete variety is finite-dimensional; Grothendieck's theorem shows that the
1482:
1470:
1434:
1411:
1374:
1289:
1268:
1138:
878:
736:
685:
644:
618:
610:
489:
466:
182:
95:
5892:
5558:
First 4 chapters from the incomplete second part of planned four-volume biography.
5024:
2535: â in algebraic geometry, an analogue of a proper map for algebraic varieties
2395:
2271:. Translated by Chaljub, Orlando. New York: Gordon and Breach Science Publishers.
1317: V, published in Ulam Quarterly in 1992â1993 and later made available on the
797:
5711:
5379:
5104:
3520:
2877:"Alexander Grothendieck (1928â2014) Mathematician who rebuilt algebraic geometry"
1346:
preface for it, in which he called Tsuji his "first true collaborator". Parts of
6215:
6171:
5909:
5719:
with photos from Grothendieck's life, given by Winfried Scharlau at IHES in 2009
5084:
2552:
2347:
2121:
1972:
1454:
1427:
1133:
1097:
1089:
942:
882:
838:
598:
343:
223:
5926:
5887:
5096:
5068:"A country of which nothing is known but the name: Grothendieck and "motives""
4231:
3535:
3196:
Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes,
2674:
2171:
The band Stone Hill All Stars have a song named after Alexander Grothendieck.
2059:
2035:
1794:
in the early 1970s after Grothendieck had largely withdrawn from mathematics.
1596:
551:
5505:
5433:
5307:
Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes
4158:"Alexandre Grothendieck, le plus grand mathématicien du XXe siÚcle, est mort"
3422:
3413:
3005:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude"
2910:
1023:
to complement it. Closely linked to these cohomology theories, he originated
5659:
5513:
5198:
5127:. "De L'analyse fonctionelle aux fondements de la géométrie algébrique". In
5100:
5088:
5045:"Un pays dont on ne connaĂźtrait que le nom (Grothendieck et les " motifs ")"
4122:
3247:"Alexandre Grothendieck, ou la mort d'un génie qui voulait se faire oublier"
3062:
2375:
1884:
1665:
1512:. Between 1949 and 1953 he worked on his doctoral thesis in this subject at
1403:
1337:
910:
805:
535:
5705:
3879:
2918:
2306:
2252:
1132:" ("a gilded cage"). While Grothendieck was at the IHĂS, opposition to the
704:
where two leading experts were working on Grothendieck's area of interest,
654:
In Le Chambon, Grothendieck attended the CollĂšge CĂ©venol (now known as the
5404:
4782:
3749:
2286:
1465:
person for at least the majority of his working life and he traveled on a
6274:
5668:
5240:
Loving and Hating Mathematics: Challenging the Myths of Mathematical Life
4993:, vol. S88, Institut des Hautes Ătudes Scientifiques, pp. 11â19
3868:] (Unpublished manuscript) (in Japanese). Translated by Tsuji Yuichi.
3121:
2457:
2400:
1838:
1705:
1606:
1541:
1493:
1420:
1085:
986:
966:
571:
514:
501:
161:
2073:
were formulated in the later 1940s as a set of mathematical problems in
1058:
The results of his work on these and other topics were published in the
5608:
3998:
Die Mutanten â Les Mutants â eine Meditation von Alexander Grothendieck
3276:[Alexander Grothendieck: A journey in pursuit of the obvious].
3274:"Alexandre Grothendieck: Un voyage Ă la poursuite des choses Ă©videntes"
2959:
David Mumford at Brown and Harvard Universities: Archive for Reprints:
2781:
2779:
1146:
1142:
578:
555:
4704:(Winter 2015 ed.). Metaphysics Research Lab, Stanford University.
3805:
Suugakusha no kodokuna bĆken : suugaku to jiko no hakken eno tabi
5671:
is a peripatetic seminar on Grothendieck view not just on mathematics
5634:
is a website devoted to the life and works of Alexandre Grothendieck.
5631:
5366:
5349:
4968:
4914:
3828:
Mathematics and the Naked King: A Dream and the Burial of Mathematics
3241:
3239:
1318:
1235:. This letter and successive parts were distributed from Bangor (see
926:
574:
567:
531:
457:. His research extended the scope of the field and added elements of
271:
67:
5600:
5406:
Wer ist Alexander Grothendieck?: Anarchie, Mathematik, SpiritualitÀt
2901:
2876:
989:. Then, following the programme he outlined in his talk at the 1958
5789:
5760:
4466:
Sheaves in Geometry and Logic: a First Introduction to Topos Theory
3441:
3439:
3297:
609:
Once, he managed to escape from the camp, intending to assassinate
449:; 28 March 1928 â 13 November 2014) was a German-born French
3481:"1953 : un « Résumé » aux développements illimités"
1852:
1105:
1024:
723:
In Nancy, he wrote his dissertation under those two professors on
563:
5566:, Somerville Massachusetts: International Press of Boston, Inc.,
3466:
Who Is Alexandre Grothendieck: Anarchy, Mathematics, Spirituality
1668:. As 'functions' these can take only the value 0, but they carry
621:. Grothendieck was permitted to live separated from his mother.
2560: â Conditions for a divisor of a local ring to be principal
1920:
denotes a kind of "meta-theory" that may be used heuristically;
1637:
5793:
3199:
Springer Science & Business Media, 2006 pp-xi-xxviii p.xii.
977:. His first (pre-IHĂS) discovery in algebraic geometry was the
5780:
Alexandre-Grothendieck-une-mathematique-en-cathedrale-gothique
5694:
3847:
A Dream and the Burial of Mathematics: The Key to Yin and Yang
2957:
Alexander Grothendieck obituary by David Mumford and John Tate
1649:'s seminar. He outlined his programme in his talk at the 1958
412:
406:
4332:"The Rising Sea: Grothendieck on simplicity and generality I"
3217:
Springer Science & Business Media, 2007 pp.237â249 p.237.
2500: â a moduli space that exists in the category of schemes
4733:
Tool and Object: A History and Philosophy of Category Theory
4041:
Les «gribouillis» d'Alexandre Grothendieck enfin sauvegardés
3214:
Vite matematiche: Protagonisti del '900, da Hilbert a Wiles,
1887:; cohomological formalism of topoi as inspiration for a new
5142:. AMS and the Société Mathématique de France. p. 600.
3528:
Foundations of Grothendieck Duality for Diagrams of Schemes
1011:
theory of schemes, providing the key tools for proving the
400:
4075:"The Mysterious Disappearance revolutionary mathematician"
2077:. They describe properties of analytic invariants, called
1790:, the last of which was settled by Grothendieck's student
1779:
reflects the topological nature of its solutions over the
1624:, which recently had been generalized to any dimension by
628:, he was sheltered and hidden in local boarding houses or
5352:
The Grothendieck I Knew: Telling, Not Hiding, Not Judging
5162:"Quelques idĂ©es maĂźtresses de l'Ćuvre de A. Grothendieck"
4489:
Dov M. Gabbay; Akihiro Kanamori; John Woods, Jr. (2012).
4098:
Unknown Quantity: A Real and Imaginary History of Algebra
3483:[1953: a "Summary" with unlimited developments].
1880:, yoga of "de Rham coefficients", "Hodge coefficients"...
1027:
theory as a generalisation of topology (relevant also in
985:
proved algebraically; in this context he also introduced
394:
5128:
4736:. Springer Science & Business Media. pp. 158â.
4626:. Springer Science & Business Media. pp. 156â.
4014:
3314:
2726:
2355: â Cartesian sections of certain fibered categories
453:
who became the leading figure in the creation of modern
4677:. Springer Science & Business Media. p. viii.
3098:
3096:
3094:
3092:
3090:
3088:
3086:
3084:
3082:
3080:
5775:
Rebellious Genius: In Memory of Alexander Grothendieck
5300:"Notes on the life and work of Alexander Grothendieck"
3824:
SĆ«gaku to hadaka no Ćsama: Aru yume to sĆ«gaku no maisĆ
3636:
3634:
3632:
3630:
3628:
3626:
3521:"Notes on derived categories and Grothendieck duality"
3038:
3036:
2821:
2819:
2817:
2815:
2813:
2811:
2798:
2796:
2794:
2710:
2708:
2706:
2704:
2702:
2700:
2698:
2696:
2694:
1640:, in 1957. It appeared in print in a paper written by
1300:. Later, it was published in two-volumes and entitled
1152:
In 1970, Grothendieck, with two other mathematicians,
278:
Produits tensoriels topologiques et espaces nucléaires
4698:
Marquis, Jean-Pierre (2015). Zalta, Edward N. (ed.).
4156:
Stéphane Foucart; Philippe Pajot (14 November 2014).
3397:(1957), "Sur quelques points d'algĂšbre homologique",
2766:
2764:
2762:
2749:
2747:
2745:
2743:
2741:
2739:
780:
Comparing Grothendieck during his Nancy years to the
415:
5785:
Les-archives-insaisissables-d-alexandre-grothendieck
5767:
Les-archives-insaisissables-d-alexandre-grothendieck
5749:
Alexander Grothendieck: A Country Known Only by Name
5744:, Winfried Scharlau, Notices of the AMS 55(8), 2008.
5140:
Grothendieck-Serre Correspondence: Bilingual Edition
3329:"Topological vector spaces, by A. Grothendieck, ..."
2537:
Pages displaying wikidata descriptions as a fallback
2502:
Pages displaying wikidata descriptions as a fallback
2477:
Pages displaying wikidata descriptions as a fallback
2405:
Pages displaying wikidata descriptions as a fallback
2380:
Pages displaying wikidata descriptions as a fallback
2366:
Pages displaying wikidata descriptions as a fallback
2357:
Pages displaying wikidata descriptions as a fallback
2208:, a main character is a student of Grothendieck's.
1664:. Grothendieck also pioneered the systematic use of
1225:, Grothendieck wrote a 600-page manuscript entitled
1137:
interested in scientific areas outside mathematics.
409:
403:
397:
5052:
Réel en mathématiques-psychanalyse et mathématiques
4596:
Michael Atiyah Collected Works: Volume 7: 2002â2013
3591:
SGA1, Springer Lecture Notes 224, p. xii, xiii
2223:
Memoirs of the American Mathematical Society Series
2128:, another algebraic analogue of topological ideas.
391:
311:
288:
270:
241:
219:
171:
148:
127:
107:
82:
53:
34:
4517:
2509: â Structure for unifying cohomology theories
2378: â proposed framework for homological algebra
2264:
1763:Grothendieck's work includes the invention of the
901:. Collaborators on the SGA projects also included
5751:, Pierre Cartier, Notices of the AMS 62(4), 2015.
5138:Colmez, Pierre; Jean-Pierre, Serre, eds. (2004).
5050:, in Cartier, Pierre; Charraud, Nathalie (eds.),
3459:"Chapter 3. From student to celebrity: 1949-1952"
3445:
3159:
2845:"Alexander Grothendieck, Math Enigma, Dies at 86"
2482:List of things named after Alexander Grothendieck
2454: â On the foundations of homological algebra
2124:, are considered the background to the theory of
1109:academia a few years later as a professor at the
613:. Later, his mother Hanka was transferred to the
585:, during this time, his parents took part in the
166:List of things named after Alexander Grothendieck
5687:at Bangor, which continued until 1991. See also
5171:, SociĂ©tĂ© MathĂ©matique de France, pp. 11â19
4547:
4545:
3599:
3597:
2843:Bruce Weber; Julie Rehmeyer (14 November 2014).
1288:(CNRS). It describes new ideas for studying the
1284:("Sketch of a Programme") for a position at the
873:Officially during this time, he had as students
762:based on them, leading to the very influential "
647:to the Germans to be sent to be murdered at the
5564:Alexandre Grothendieck: A Mathematical Portrait
4620:M. Ram Murty; V. Kumar Murty (6 October 2012).
1771:theories, which explain an observation made by
1672:information, in purely algebraic settings. His
1198:La Longue Marche à travers la théorie de Galois
1031:). He also provided, by means of a categorical
826:
477:led to revolutionary advances in many areas of
5416:Who is Alexander Grothendieck? Part 1: Anarchy
4671:Marc Levine; Fabien Morel (23 February 2007).
4623:The Mathematical Legacy of Srinivasa Ramanujan
4060:Institut Montpelliérain Alexander Grothendieck
2140:across varied mathematical structures brought
1908:"Schematic" or "arithmetic" point of view for
1595:and others, after sheaves had been defined by
1508:Grothendieck's early mathematical work was in
1062:and in less polished form in the notes of the
5805:
5410:First part of planned four-volume biography.
5011:Bulletin of the American Mathematical Society
3843:Aru yume to sĆ«gaku no maisĆ: In to yĆ no kagi
3651:
3649:
3336:Bulletin of the American Mathematical Society
2229:. Providence: American Mathematical Society.
1786:This program culminated in the proofs of the
1756:), which gathers together talks given in the
1632:was announced by Grothendieck at the initial
1620:In 1956, he applied the same thinking to the
731:in Brazil, where he immigrated by means of a
669:Studies and contact with research mathematics
8:
5485:Notices of the American Mathematical Society
5358:Notices of the American Mathematical Society
5287:Notices of the American Mathematical Society
5267:Notices of the American Mathematical Society
5054:(in French), Editions Agalma, archived from
4955:Notices of the American Mathematical Society
4901:Notices of the American Mathematical Society
4492:Sets and Extensions in the Twentieth Century
4441:
4396:
3919:"Crafoord Prize letter, English translation"
3671:
1286:Centre National de la Recherche Scientifique
979:GrothendieckâHirzebruchâRiemannâRoch theorem
781:
689:
5708:, French originals and Spanish translations
4565:, vol. 52, New York: Springer-Verlag,
3880:"RĂ©coltes et Semailles; La Clef des Songes"
3574:The Life and Work of Alexander Grothendieck
3381:
3053:
3051:
2403: â class of special local-convex space
2050:. As part of this project, his creation of
1217:In 1983, stimulated by correspondence with
1055:, which were further developed by Verdier.
853:In 1958, Grothendieck was installed at the
5812:
5798:
5790:
5689:Alexander Grothendieck: some recollections
5237:Hersh, Reuben; John-Steiner, Vera (2011).
4947:"Alexandre Grothendieck 1928â2014, Part 2"
4893:"Alexandre Grothendieck 1928â2014, Part 1"
4831:: CS1 maint: location missing publisher (
4599:. Oxford University Press. pp. 383â.
4452:
4450:
2002:related topological properties of complex
1039:of schemes giving birth to the now famous
42:
31:
5365:
5023:
4967:
4913:
4290:
4101:. National Academies Press. p. 314.
3496:
3494:
3412:
3347:
3296:
2900:
2448: â Local ring in commutative algebra
2054:, a category-theoretic generalization of
1570:Sur quelques points d'algĂšbre homologique
1278:In 1984, Grothendieck wrote the proposal
1088:. He strongly opposed both United States
5755:Alexandre Grothendieck 1928â2014, Part 1
5725:âbiographical sketch of Grothendieck by
3982:
3207:
3205:
3174:
3172:
3170:
3168:
3147:
3135:
3102:
2825:
2802:
2714:
2589:Standard conjectures on algebraic cycles
1692:, and close analogues of the methods of
1651:International Congress of Mathematicians
1324:In the extensive autobiographical work,
991:International Congress of Mathematicians
855:Institut des hautes Ă©tudes scientifiques
542:(also known as Alexander Tanaroff), had
486:Institut des hautes Ă©tudes scientifiques
473:to its foundations, while his so-called
48:Alexander Grothendieck in Montréal, 1970
6383:German people of Russian-Jewish descent
5712:English summary of "La Clef des Songes"
5649:MacTutor History of Mathematics Archive
5031:
4847:"CORMAC MCCARTHY HAS NEVER BEEN BETTER"
4701:The Stanford Encyclopedia of Philosophy
4314:
4251:
4249:
3640:
3369:
3042:
2952:
2950:
2948:
2838:
2836:
2834:
2785:
2770:
2753:
2690:
2641:
2136:Grothendieck's emphasis on the role of
1912:and regular configurations of all kinds
5545:
5477:"Who is Alexander Grothendieck ?"
5323:"Sensitivity to the Harmony of Things"
4824:
4524:. Cambridge University Press. p.
4208:from the original on 29 September 2014
3226:
3027:
2120:'s work, and Grothendieck's theory of
2018:, topological K-theory was founded by
1580:and applied their theory to show that
1231:. It began with a letter addressed to
656:Le CollÚge-Lycée Cévenol International
6363:Emigrants from Nazi Germany to France
5723:Can one explain schemes to biologists
5475:Scharlau, Winfried (September 2008).
5176:Douroux, Philippe (8 February 2012).
4945:; Coordinating Editors (April 2016).
4891:; Coordinating Editors (March 2016).
4809:When we cease to understand the world
4384:
4302:
2961:Can one explain schemes to biologists
2489: â Concept in algebraic geometry
2180:When We Cease to Understand the World
2100:Grothendieck's conjectural theory of
1982:that informally can be thought of as
1749:Fondements de la Géometrie Algébrique
1492:He had five children: a son with his
1419:, a small village at the foot of the
1160:, created a political group entitled
444:
427:
7:
4979:from the original on 9 October 2022.
4925:from the original on 9 October 2022.
3563:from the original on 9 October 2022.
3359:from the original on 9 October 2022.
3272:Philippe Douroux (8 February 2012).
3017:from the original on 9 October 2022.
2149:is now the basic object of study in
1760:, also contains important material.
1373:. Influenced by the Catholic mystic
1306:(Cambridge University Press, 1997).
1202:The Long March Through Galois Theory
1080:Grothendieck's political views were
5316:from the original on 9 October 2022
4411:"Correspondance Grothendieck-Serre"
4344:from the original on 9 October 2022
4274:"Alexander Grothendieck - obituary"
4027:Le trésor oublié du génie des maths
3964:from the original on 9 October 2022
3894:"Free books: RĂ©coltes et semailles"
3784:from the original on 9 October 2022
3772:"Chapter 23. RĂ©coltes et Semailles"
2034:Grothendieck's construction of new
1397:Retirement into reclusion and death
1353:In 1988, Grothendieck declined the
1236:
933:there as well. Many others such as
504:. He later became professor at the
6348:20th-century French mathematicians
5632:https://www.grothendieckcircle.org
3479:Guillaume Aubrun (17 March 2020).
2984:from the original on 22 March 2019
2669:and, with the Dutch mathematician
2624:Vector bundles on algebraic curves
2427: â Concept in category theory
635:His father was arrested under the
429:[ËalÉËksandÉËÉĄÊoËtnÌ©ËdiËk]
25:
5757:, Notices of the AMS 63(3), 2016.
5582:"Faisceaux algébriques cohérents"
5444:"Wer ist Alexander Grothendieck?"
3750:"Visiting Alexandre Grothendieck"
3184:Basic Books, 2009 pp.8ff.pp.8â15.
3181:The Artist and the Mathematician,
2661:Ruelle invented the concept of a
1883:"Topological algebra": â-stacks,
1836:GrothendieckâRiemannâRoch theorem
1739:Séminaire de géométrie algébrique
1630:GrothendieckâRiemannâRoch theorem
1605:(pairs of varieties related by a
1485:that she contracted in camps for
1461:after the war. Thus, he became a
1457:in 1945 and he did not apply for
1065:Séminaire de géométrie algébrique
997:, developing it in detail in his
684:Initially, Grothendieck attended
6311:
6302:
6301:
5681:The origins of 'Pursuing Stacks'
5216:Grothendieck, Alexander (1986).
5193:Grothendieck, Alexander (2022).
4520:Undergraduate Algebraic Geometry
4468:. Springer-Verlag New York Inc.
4363:Peck, Morgen (31 January 2007).
3860:Grothendieck, Alexander (1998).
3841:Grothendieck, Alexander (2016).
3822:Grothendieck, Alexander (2015).
3803:Grothendieck, Alexander (2015).
3503:The Artist and the Mathematician
3059:"The Early Background of Genius"
2387: â Homological construction
1802:In Grothendieck's retrospective
1798:Major mathematical contributions
1729:ĂlĂ©ments de gĂ©omĂ©trie algĂ©brique
1524:. His key contributions include
1188:Manuscripts written in the 1980s
1072:) that he directed at the IHĂS.
1000:ĂlĂ©ments de gĂ©omĂ©trie algĂ©brique
788:-trained students at that time (
769:In 1957 he was invited to visit
387:
27:French mathematician (1928â2014)
4715:S. Gelfand; Yuri Manin (1988).
4593:Michael Atiyah (3 April 2014).
4516:Miles Reid (15 December 1988).
4409:Michel Raynaud (October 2003).
3862:MaisĆ (3) aruiwa yottsu no sĆsa
3349:10.1090/S0002-9904-1976-14076-1
3115:Philippe Douroux (6 May 2019).
2058:, has influenced the fields of
1196:Produced during 1980 and 1981,
983:HirzebruchâRiemannâRoch theorem
839:EinsteinâPodolskyâRosen paradox
5742:Who Is Alexander Grothendieck?
5469:A review of the German edition
5321:Rehmeyer, Julie (9 May 2008),
5243:. Princeton University Press.
4717:Methods of homological algebra
3582:, vol. 113, no. 9, footnote 6.
1210:. It also includes a study of
993:, he introduced the theory of
643:, and then handed over by the
1:
5664:Mathematics Genealogy Project
5498:American Mathematical Society
5025:10.1090/S0273-0979-01-00913-2
4730:Ralph Krömer (25 June 2007).
4660:. Princeton University Press.
4563:Graduate Texts in Mathematics
4073:Galchen, Rivka (9 May 2022).
3866:Burial (3) or Four Operations
3604:Jackson, Allyn (March 1999).
3579:American Mathematical Monthly
3446:Hersh & John-Steiner 2011
3403:, Second Series (in French),
3253:(in French). 13 November 2014
3160:Hersh & John-Steiner 2011
1660:, which led to the theory of
1576:in 1957) where he introduced
1564:, producing the influential "
1035:, an algebraic definition of
637:Vichy anti-Jewish legislation
156:and synthesis between it and
5562:Schneps, Leila, ed. (2014),
5305:, in Pragracz, Piotr (ed.),
5197:(in French). Paris, France:
4365:"Equality of Mathematicians"
2339: â Mathematical concept
1900:anabelian algebraic geometry
1819:"Continuous" and "discrete"
1696:, all in an integrated way.
1094:Soviet military expansionism
1021:algebraic de Rham cohomology
649:Auschwitz concentration camp
548:Johanna "Hanka" Grothendieck
5580:Serre, Jean-Pierre (1955).
5528:Scharlau, Winfried (2010).
5449:(in German). pp. 1â22.
5442:Scharlau, Winfried (n.d.).
5414:Scharlau, Winfried (2011).
5403:Scharlau, Winfried (2007),
5225:(in French). Archived from
4869:Sources and further reading
3400:Tohoku Mathematical Journal
3327:HorvĂąth, John (July 1976).
2673:, produced a new model for
2609:Theorem on formal functions
2507:Motive (algebraic geometry)
2452:Grothendieck's TĂŽhoku paper
1873:(Grothendieck â-categories)
1811:Topological tensor products
1634:Mathematische Arbeitstagung
1574:Tohoku Mathematical Journal
1526:topological tensor products
1380:Lettre de la Bonne Nouvelle
1164:âthe name later changed to
1104:in the forests surrounding
1051:theory, he also introduced
663:Righteous Among the Nations
540:Alexander "Sascha" Schapiro
249:Institut des hautes Ă©tudes
6424:
5386:Princeton University Press
5360:(August 2019): 1069â1077.
4807:Labatut, BenjamĂn (2020).
3711:"Publication Announcement"
2604:Theorem of absolute purity
2574:Semistable abelian variety
1584:may be defined as certain
981:, a generalisation of the
6297:
5827:
5381:The Mathematician's Brain
5125:Dieudonné, Jean Alexandre
4495:. Elsevier. p. 733.
4424:(9): 1086. Archived from
3950:Grothendieck, Alexander.
3684:Grothendieck, Alexandre.
3536:10.1007/978-3-540-85420-3
2544: â Seminal math text
2528:Projective tensor product
2267:Topological Vector Spaces
2085:, the first example of a
1904:GaloisâTeichmĂŒller theory
1540:, and the application of
1530:topological vector spaces
1449:Grothendieck was born in
1111:University of Montpellier
1096:. To protest against the
1047:. As a framework for his
782:
758:and the reformulation of
706:topological vector spaces
690:
675:University of Montpellier
530:Grothendieck was born in
506:University of Montpellier
372:
257:University of Montpellier
212:
135:University of Montpellier
41:
5654:University of St Andrews
5644:"Alexander Grothendieck"
5278:Jackson, Allyn (2004b),
5258:Jackson, Allyn (2004a),
5178:"Alexandre Grothendieck"
4783:"Alexander Grothendieck"
3655:Alexandre Grothendieck,
3485:Images des Mathématiques
3278:Images des mathématiques
2558:RamanujamâSamuel theorem
2523:Parafactorial local ring
2473:Infinitesimal cohomology
2441:Fundamental group scheme
1387:Grothendieck Festschrift
1303:Geometric Galois Actions
1122:visiteur de longue durée
1045:fundamental group scheme
877:(who worked on SGA3, on
784:Ăcole Normale SupĂ©rieure
692:Ăcole Normale SupĂ©rieure
492:in 1966 for advances in
6388:Nancy-Université alumni
5700:"RĂ©coltes et Semailles"
5538:Schneps, Leila (n.d.).
5298:Pragacz, Piotr (2005),
5030:English translation of
4180:Secret Blogging Seminar
4176:"Grothendieck's letter"
4127:"The Einstein of maths"
3686:"RĂ©coltes et Semailles"
3657:Esquisse d'un Programme
3395:Grothendieck, Alexander
3382:Colmez & Serre 2004
2614:Ultrabornological space
2410:DunfordâPettis property
2261:Grothendieck, Alexander
2219:Grothendieck, Alexander
2110:motivic homotopy theory
2083:â-adic Ă©tale cohomology
2040:algebraic number theory
1281:Esquisse d'un Programme
1265:motivic homotopy theory
1207:Esquisse d'un programme
1090:intervention in Vietnam
1041:Ă©tale fundamental group
835:Grothendieck inequality
729:University of SĂŁo Paulo
645:French Vichy government
262:University of SĂŁo Paulo
6403:Scientists from Berlin
5669:SĂ©minaire Grothendieck
5660:Alexander Grothendieck
3725:"Harvests and Sowings"
3501:Amir D. Aczel (2009).
3414:10.2748/tmj/1178244839
2629:Zariski's main theorem
2362:Crystalline cohomology
2337:Approximation property
1955:
1878:crystalline cohomology
1602:relative point of view
1538:Schwartz distributions
1100:, he gave lectures on
1017:crystalline cohomology
831:
742:Grothendieck moved to
641:Drancy internment camp
475:"relative" perspective
383:Alexandre Grothendieck
379:Alexander Grothendieck
120:(post 1945 until 1971)
36:Alexander Grothendieck
18:Alexandre Grothendieck
5736:Archives Grothendieck
5702:, Spanish translation
5695:RĂ©coltes et Semailles
5589:Annals of Mathematics
5129:Cartier et al. (2007)
5065:English translation:
4202:"Grothendieck Circle"
2788:, p. 10, footnote 12.
2548:Quasi-finite morphism
2391:Descent (mathematics)
2353:Crystal (mathematics)
2048:representation theory
1950:
1804:RĂ©coltes et Semailles
1348:RĂ©coltes et Semailles
1336:will be published by
1330:RĂ©coltes et Semailles
1326:RĂ©coltes et Semailles
1311:Bertini-type theorems
931:nonabelian cohomology
929:theory extensions of
885:(cotangent complex),
718:locally convex spaces
626:Le Chambon-sur-Lignon
617:for the remainder of
538:parents. His father,
5706:"La Clef des Songes"
5640:Robertson, Edmund F.
5552:: CS1 maint: year (
4280:on 15 November 2014.
3995:Scharlau, Winfried,
3952:"La Clef des Songes"
3770:Scharlau, Winfried.
3003:Scharlau, Winfried.
2974:"Fields Medals 1966"
2564:Scheme (mathematics)
2436:Fundamental groupoid
2138:universal properties
2079:local zeta functions
2024:Friedrich Hirzebruch
2012:topological K-theory
2000:RiemannâRoch theorem
1871:motivic Galois group
1622:RiemannâRoch theorem
1615:higher direct images
1536:as foundational for
1500:in the early 1970s.
1455:fall of Nazi Germany
1439:Saint-Girons, AriĂšge
1247:and prospects for a
949:were also involved.
615:Gurs internment camp
526:Family and childhood
6378:Functional analysts
6353:Algebraic geometers
5675:Grothendieck Circle
5638:O'Connor, John J.;
5418:. Books on Demand.
5354:By Paulo Ribenboim"
5333:on 16 February 2012
4674:Algebraic Cobordism
4656:J.S. Milne (1980).
4228:"RĂ©Ă©dition des SGA"
4058:[Welcome].
4015:Cartier et al. 2007
3661:English translation
3606:"The IHĂS at Forty"
3315:Cartier et al. 2007
3251:Libération Sciences
2933:"Guardian obituary"
2893:2015Natur.517..272M
2727:Cartier et al. 2007
2599:Tannakian formalism
2594:Sketch of a program
2584:Stack (mathematics)
2468:Homotopy hypothesis
2431:Formally smooth map
2343:BarsottiâTate group
2322:Accessible category
2188:National Book Award
2151:homological algebra
2126:algebraic cobordism
2114:motivic integration
2075:arithmetic geometry
2030:Cohomology theories
1889:homotopical algebra
1843:intersection theory
1690:commutative algebra
1678:birational geometry
1572:, published in the
1562:homological algebra
1552:It is, however, in
1510:functional analysis
1321:web site in 2004).
1319:Grothendieck Circle
1173:temporary professor
893:(co-founder of the
752:homological algebra
725:functional analysis
702:University of Nancy
498:homological algebra
463:homological algebra
459:commutative algebra
446:[ÉĄÊÉtÉndik]
236:homological algebra
228:functional analysis
140:University of Nancy
6398:Operator theorists
6317:Mathematics portal
5717:Video of a lecture
5232:on 18 August 2017.
4758:"Colonel LĂĄgrimas"
4558:Algebraic Geometry
4431:on 3 October 2003.
4418:Notices of the AMS
3613:Notices of the AMS
3487:(in French). CNRS.
3280:(in French). CNRS.
2963:, 14 December 2014
2857:on 1 January 2022.
2849:The New York Times
2569:Section conjecture
2415:Effaceable functor
2327:Algebraic geometry
2184:Shinichi Mochizuki
2157:In popular culture
2106:algebraic K-theory
2064:mathematical logic
2056:point-set topology
2044:algebraic topology
2016:Bonn Arbeitstagung
1984:topological spaces
1825:derived categories
1758:SĂ©minaire Bourbaki
1746:). The collection
1694:algebraic topology
1680:, techniques from
1578:abelian categories
1554:algebraic geometry
1459:French citizenship
1362:La Clef des Songes
1298:anabelian geometry
1273:Vladimir Voevodsky
1245:algebraic geometry
1221:and Tim Porter at
1212:TeichmĂŒller theory
1076:Political activism
1053:derived categories
1037:fundamental groups
959:algebraic geometry
891:Jean-Louis Verdier
771:Harvard University
756:abelian categories
748:algebraic topology
700:, he moved to the
639:, and sent to the
624:In the village of
494:algebraic geometry
455:algebraic geometry
364:Jean-Louis Verdier
232:algebraic geometry
192:Ămile Picard Medal
154:algebraic geometry
6325:
6324:
5573:978-1-57146-282-4
5149:978-1-4704-6939-9
5116:978-0-8176-4566-3
5101:Ribet, Kenneth A.
5089:Katz, Nicholas M.
4818:978-1-68137-566-3
4743:978-3-7643-7524-9
4684:978-3-540-36824-3
4633:978-81-322-0769-6
4606:978-0-19-968926-2
4572:978-0-387-90244-9
4553:Hartshorne, Robin
4535:978-0-521-35662-6
4502:978-0-444-51621-3
4458:Saunders Mac Lane
4442:Grothendieck 1986
4397:Grothendieck 1986
4182:. 9 February 2010
4137:on 11 August 2016
4125:(20 March 2004).
3931:on 6 January 2006
3672:Grothendieck 2022
3545:978-3-540-85419-7
2938:Independent.co.uk
2677:during the 1970s.
2663:strange attractor
2278:978-0-677-30020-7
2236:978-0-8218-1216-7
2095:Langlands program
1998:of the classical
1910:regular polyhedra
1862:l-adic cohomology
1769:l-adic cohomology
1674:theory of schemes
1593:Jean-Pierre Serre
1588:in this context.
1504:Mathematical work
1487:displaced persons
1406:. At some point,
1223:Bangor University
1177:CollĂšge de France
1166:Survivre et vivre
1029:categorical logic
919:Lefschetz pencils
818:Bernard Malgrange
814:Jean-Pierre Serre
587:Spanish Civil War
583:Winfried Scharlau
554:German family in
376:
375:
312:Doctoral students
290:Doctoral advisors
214:Scientific career
114:French since 1971
16:(Redirected from
6415:
6408:Stateless people
6393:Nicolas Bourbaki
6373:French pacifists
6368:Fields Medalists
6315:
6305:
6304:
5821:Fields Medalists
5814:
5807:
5800:
5791:
5772:Kutateladze S.S.
5763:by Mateo Carmona
5656:
5620:
5586:
5576:
5557:
5551:
5543:
5533:
5524:
5522:
5520:
5481:
5468:
5450:
5448:
5438:English version.
5437:
5409:
5399:
5371:
5369:
5367:10.1090/noti1909
5346:Ribenboim, Paulo
5341:
5340:
5338:
5329:, archived from
5317:
5315:
5304:
5294:
5284:
5274:
5264:
5254:
5233:
5231:
5224:
5212:
5189:
5187:
5185:
5172:
5166:
5153:
5132:
5120:
5103:, eds. (2007) .
5074:
5072:
5062:
5060:
5049:
5029:
5027:
5007:
4994:
4980:
4978:
4971:
4969:10.1090/noti1361
4951:
4926:
4924:
4917:
4915:10.1090/noti1336
4897:
4862:
4861:
4859:
4857:
4843:
4837:
4836:
4830:
4822:
4811:. New York, NY.
4804:
4798:
4797:
4795:
4793:
4779:
4773:
4772:
4770:
4768:
4754:
4748:
4747:
4727:
4721:
4720:
4712:
4706:
4705:
4695:
4689:
4688:
4668:
4662:
4661:
4658:Ătale cohomology
4653:
4647:
4644:
4638:
4637:
4617:
4611:
4610:
4590:
4584:
4583:
4549:
4540:
4539:
4523:
4513:
4507:
4506:
4486:
4480:
4479:
4454:
4445:
4439:
4433:
4432:
4430:
4415:
4406:
4400:
4394:
4388:
4382:
4376:
4375:
4360:
4354:
4353:
4351:
4349:
4343:
4336:
4324:
4318:
4312:
4306:
4300:
4294:
4288:
4282:
4281:
4276:. Archived from
4270:
4264:
4253:
4244:
4243:
4241:
4239:
4230:. Archived from
4224:
4218:
4217:
4215:
4213:
4198:
4192:
4191:
4189:
4187:
4172:
4166:
4165:
4153:
4147:
4146:
4144:
4142:
4133:. Archived from
4119:
4113:
4112:
4089:
4083:
4082:
4070:
4064:
4063:
4052:
4046:
4045:
4038:
4032:
4031:
4024:
4018:
4012:
4006:
4005:
4003:
3992:
3986:
3980:
3974:
3973:
3971:
3969:
3963:
3956:
3947:
3941:
3940:
3938:
3936:
3930:
3924:. Archived from
3923:
3915:
3909:
3908:
3906:
3904:
3890:
3884:
3883:
3876:
3870:
3869:
3857:
3851:
3850:
3838:
3832:
3831:
3819:
3813:
3812:
3800:
3794:
3793:
3791:
3789:
3783:
3776:
3767:
3761:
3760:
3758:
3756:
3745:
3739:
3738:
3736:
3734:
3729:
3721:
3715:
3714:
3707:
3701:
3700:
3698:
3696:
3690:
3681:
3675:
3669:
3663:
3653:
3644:
3638:
3621:
3620:
3610:
3601:
3592:
3589:
3583:
3571:
3565:
3564:
3562:
3525:
3513:
3507:
3506:
3498:
3489:
3488:
3476:
3470:
3469:
3463:
3455:
3449:
3443:
3434:
3433:
3416:
3391:
3385:
3379:
3373:
3367:
3361:
3360:
3358:
3351:
3334:. Book Reviews.
3333:
3324:
3318:
3312:
3303:
3302:
3300:
3288:
3282:
3281:
3269:
3263:
3262:
3260:
3258:
3243:
3234:
3224:
3218:
3209:
3200:
3191:
3185:
3176:
3163:
3157:
3151:
3145:
3139:
3133:
3127:
3126:
3112:
3106:
3100:
3075:
3074:
3072:
3070:
3061:. Archived from
3055:
3046:
3040:
3031:
3025:
3019:
3018:
3016:
3009:
3000:
2994:
2993:
2991:
2989:
2970:
2964:
2954:
2943:
2942:
2929:
2923:
2922:
2904:
2865:
2859:
2858:
2856:
2851:. Archived from
2840:
2829:
2823:
2806:
2800:
2789:
2783:
2774:
2768:
2757:
2751:
2734:
2724:
2718:
2712:
2678:
2667:dynamical system
2659:
2653:
2646:
2619:Weil conjectures
2579:Sheaf cohomology
2538:
2513:Nuclear operator
2503:
2493:Nakai conjecture
2487:Local cohomology
2478:
2406:
2385:Derived category
2381:
2367:
2358:
2317:Abelian category
2290:
2270:
2256:
2176:BenjamĂn Labatut
2162:Colonel LĂĄgrimas
2147:abelian category
2071:Weil conjectures
2004:algebraic curves
1988:commutative ring
1969:algebraic curves
1858:Ătale cohomology
1788:Weil conjectures
1647:Claude Chevalley
1586:derived functors
1582:sheaf cohomology
1532:, the theory of
1522:Laurent Schwartz
1516:, supervised by
1417:Lasserre, AriĂšge
1371:Bernhard Riemann
1154:Claude Chevalley
1126:Bures-sur-Yvette
1049:coherent duality
1013:Weil conjectures
1009:Ă©tale cohomology
975:complex analysis
939:Robin Hartshorne
915:monodromy theory
907:Ă©tale cohomology
895:derived category
787:
786:
760:sheaf cohomology
744:Lawrence, Kansas
714:Laurent Schwartz
695:
694:
679:Lebesgue measure
479:pure mathematics
448:
443:
439:
438:
437:
431:
426:
422:
421:
418:
417:
414:
411:
408:
405:
402:
399:
396:
393:
319:Pierre Berthelot
298:Laurent Schwartz
284:
205:
198:
189:
180:
92:
90:
87:13 November 2014
63:
61:
46:
32:
21:
6423:
6422:
6418:
6417:
6416:
6414:
6413:
6412:
6328:
6327:
6326:
6321:
6293:
6292:
6289:
6262:
6235:
6208:
6181:
6154:
6137:
6110:
6083:
6056:
6034:
6012:
5985:
5968:
5941:
5914:
5897:
5880:
5863:
5846:
5823:
5818:
5761:A. Grothendieck
5637:
5628:
5623:
5601:10.2307/1969915
5584:
5579:
5574:
5561:
5544:
5537:
5527:
5518:
5516:
5479:
5474:
5453:
5446:
5441:
5426:
5413:
5402:
5396:
5374:
5344:
5336:
5334:
5320:
5313:
5302:
5297:
5293:(10): 1196â1212
5282:
5277:
5262:
5257:
5251:
5236:
5229:
5222:
5215:
5209:
5192:
5183:
5181:
5175:
5164:
5158:Deligne, Pierre
5156:
5150:
5137:
5123:
5117:
5081:Cartier, Pierre
5079:
5070:
5066:
5061:on 4 March 2016
5058:
5047:
5041:Cartier, Pierre
5039:
5005:
4999:Cartier, Pierre
4997:
4985:Cartier, Pierre
4983:
4976:
4962:(4): 401â2413.
4949:
4929:
4922:
4895:
4875:
4871:
4866:
4865:
4855:
4853:
4845:
4844:
4840:
4823:
4819:
4806:
4805:
4801:
4791:
4789:
4781:
4780:
4776:
4766:
4764:
4756:
4755:
4751:
4744:
4729:
4728:
4724:
4714:
4713:
4709:
4697:
4696:
4692:
4685:
4670:
4669:
4665:
4655:
4654:
4650:
4645:
4641:
4634:
4619:
4618:
4614:
4607:
4592:
4591:
4587:
4573:
4551:
4550:
4543:
4536:
4515:
4514:
4510:
4503:
4488:
4487:
4483:
4476:
4456:
4455:
4448:
4440:
4436:
4428:
4416:. Book Review.
4413:
4408:
4407:
4403:
4395:
4391:
4383:
4379:
4362:
4361:
4357:
4347:
4345:
4341:
4334:
4326:
4325:
4321:
4313:
4309:
4301:
4297:
4289:
4285:
4272:
4271:
4267:
4254:
4247:
4237:
4235:
4234:on 29 June 2016
4226:
4225:
4221:
4211:
4209:
4200:
4199:
4195:
4185:
4183:
4174:
4173:
4169:
4155:
4154:
4150:
4140:
4138:
4121:
4120:
4116:
4109:
4093:John Derbyshire
4091:
4090:
4086:
4072:
4071:
4067:
4054:
4053:
4049:
4043:
4039:
4035:
4029:
4025:
4021:
4013:
4009:
4001:
3994:
3993:
3989:
3981:
3977:
3967:
3965:
3961:
3954:
3949:
3948:
3944:
3934:
3932:
3928:
3921:
3917:
3916:
3912:
3902:
3900:
3892:
3891:
3887:
3878:
3877:
3873:
3859:
3858:
3854:
3840:
3839:
3835:
3821:
3820:
3816:
3802:
3801:
3797:
3787:
3785:
3781:
3774:
3769:
3768:
3764:
3754:
3752:
3747:
3746:
3742:
3732:
3730:
3727:
3723:
3722:
3718:
3709:
3708:
3704:
3694:
3692:
3688:
3683:
3682:
3678:
3670:
3666:
3654:
3647:
3639:
3624:
3608:
3603:
3602:
3595:
3590:
3586:
3572:
3568:
3560:
3546:
3523:
3515:
3514:
3510:
3500:
3499:
3492:
3478:
3477:
3473:
3461:
3457:
3456:
3452:
3444:
3437:
3393:
3392:
3388:
3380:
3376:
3368:
3364:
3356:
3331:
3326:
3325:
3321:
3313:
3306:
3290:
3289:
3285:
3271:
3270:
3266:
3256:
3254:
3245:
3244:
3237:
3225:
3221:
3210:
3203:
3192:
3188:
3177:
3166:
3158:
3154:
3146:
3142:
3134:
3130:
3114:
3113:
3109:
3101:
3078:
3068:
3066:
3065:on 15 June 2011
3057:
3056:
3049:
3041:
3034:
3026:
3022:
3014:
3007:
3002:
3001:
2997:
2987:
2985:
2972:
2971:
2967:
2955:
2946:
2931:
2930:
2926:
2902:10.1038/517272a
2867:
2866:
2862:
2842:
2841:
2832:
2824:
2809:
2801:
2792:
2784:
2777:
2769:
2760:
2752:
2737:
2725:
2721:
2713:
2692:
2687:
2682:
2681:
2660:
2656:
2647:
2643:
2638:
2633:
2542:Pursuing Stacks
2536:
2533:Proper morphism
2501:
2476:
2446:Gorenstein ring
2425:Fibred category
2404:
2379:
2365:
2356:
2332:Algebraic stack
2297:
2279:
2259:
2237:
2217:
2214:
2202:and its sequel
2194:Cormac McCarthy
2159:
2142:category theory
2134:
2132:Category theory
2116:. This theory,
2087:Weil cohomology
2032:
1964:
1938:
1800:
1781:complex numbers
1724:
1702:learned journal
1506:
1479:
1467:Nansen passport
1447:
1399:
1294:dessin d'enfant
1261:Pursuing Stacks
1257:Les DĂ©rivateurs
1241:homotopy theory
1228:Pursuing Stacks
1190:
1102:category theory
1078:
971:category theory
955:
875:Michel Demazure
868:learned journal
851:
843:quantum physics
802:Jacques Dixmier
733:Nansen passport
671:
595:
581:. According to
577:and teacher in
528:
523:
471:category theory
441:
434:
433:
432:
424:
390:
386:
368:
359:HoĂ ng XuĂąn SĂnh
349:William Messing
329:Michel Demazure
307:
282:
266:
250:
208:
203:
196:
187:
178:
164:
144:
128:Alma mater
123:
103:
93:
88:
86:
78:
65:
59:
57:
49:
37:
28:
23:
22:
15:
12:
11:
5:
6421:
6419:
6411:
6410:
6405:
6400:
6395:
6390:
6385:
6380:
6375:
6370:
6365:
6360:
6355:
6350:
6345:
6340:
6330:
6329:
6323:
6322:
6320:
6319:
6309:
6298:
6295:
6294:
6291:
6290:
6288:
6287:
6282:
6277:
6272:
6265:
6263:
6261:
6260:
6255:
6250:
6245:
6238:
6236:
6234:
6233:
6228:
6223:
6218:
6211:
6209:
6207:
6206:
6201:
6196:
6191:
6184:
6182:
6180:
6179:
6174:
6169:
6164:
6157:
6155:
6153:
6152:
6147:
6140:
6138:
6136:
6135:
6130:
6125:
6120:
6113:
6111:
6109:
6108:
6103:
6098:
6093:
6086:
6084:
6082:
6081:
6076:
6071:
6066:
6059:
6057:
6055:
6054:
6049:
6044:
6037:
6035:
6033:
6032:
6027:
6022:
6015:
6013:
6011:
6010:
6005:
6000:
5995:
5988:
5986:
5984:
5983:
5978:
5971:
5969:
5967:
5966:
5961:
5956:
5951:
5944:
5942:
5940:
5939:
5934:
5929:
5924:
5917:
5915:
5913:
5912:
5907:
5900:
5898:
5896:
5895:
5890:
5883:
5881:
5879:
5878:
5873:
5866:
5864:
5862:
5861:
5856:
5849:
5847:
5845:
5844:
5839:
5832:
5829:
5828:
5825:
5824:
5819:
5817:
5816:
5809:
5802:
5794:
5788:
5787:
5782:
5777:
5769:
5764:
5758:
5752:
5745:
5738:
5733:
5720:
5714:
5709:
5703:
5697:
5692:
5678:
5672:
5666:
5657:
5635:
5627:
5626:External links
5624:
5622:
5621:
5595:(2): 197â278.
5577:
5572:
5559:
5535:
5525:
5494:Providence, RI
5472:
5471:
5470:
5451:
5439:
5425:978-3842340923
5424:
5400:
5395:978-0691129822
5394:
5372:
5350:"Excerpt from
5342:
5318:
5309:, BirkhÀuser,
5295:
5275:
5273:(4): 1038â1056
5255:
5250:978-1400836116
5249:
5234:
5213:
5208:978-2073004833
5207:
5190:
5173:
5154:
5148:
5135:
5134:
5133:
5115:
5109:. BirkhÀuser.
5097:Manin, Yuri I.
5093:Laumon, GĂ©rard
5077:
5076:
5075:
5037:
5036:
5035:
5032:Cartier (1998)
5018:(4): 389â408.
4981:
4927:
4908:(3): 242â255.
4872:
4870:
4867:
4864:
4863:
4838:
4817:
4799:
4774:
4762:Restless Books
4749:
4742:
4722:
4707:
4690:
4683:
4663:
4648:
4639:
4632:
4612:
4605:
4585:
4571:
4541:
4534:
4508:
4501:
4481:
4474:
4446:
4434:
4401:
4389:
4377:
4355:
4328:McLarty, Colin
4319:
4307:
4295:
4291:Dieudonné 2007
4283:
4265:
4263:31 August 2024
4245:
4219:
4193:
4167:
4148:
4114:
4107:
4084:
4079:The New Yorker
4065:
4047:
4033:
4019:
4007:
3987:
3985:, p. 940.
3975:
3942:
3910:
3885:
3871:
3852:
3833:
3814:
3795:
3762:
3740:
3716:
3702:
3676:
3664:
3645:
3622:
3593:
3584:
3566:
3544:
3517:Lipman, Joseph
3508:
3505:. Basic Books.
3490:
3471:
3468:. Vol. 2.
3450:
3448:, p. 113.
3435:
3407:(2): 119â221,
3386:
3374:
3362:
3342:(4): 515â521.
3319:
3304:
3283:
3264:
3235:
3219:
3201:
3186:
3178:Amir D. Aczel,
3164:
3162:, p. 109.
3152:
3140:
3138:, p. 931.
3128:
3107:
3076:
3047:
3032:
3020:
2995:
2965:
2944:
2924:
2869:Mumford, David
2860:
2830:
2807:
2790:
2775:
2758:
2735:
2719:
2689:
2688:
2686:
2683:
2680:
2679:
2654:
2650:Pierre Cartier
2640:
2639:
2637:
2634:
2632:
2631:
2626:
2621:
2616:
2611:
2606:
2601:
2596:
2591:
2586:
2581:
2576:
2571:
2566:
2561:
2555:
2550:
2545:
2539:
2530:
2525:
2520:
2515:
2510:
2504:
2495:
2490:
2484:
2479:
2470:
2465:
2463:Hilbert scheme
2460:
2455:
2449:
2443:
2438:
2433:
2428:
2422:
2420:Excellent ring
2417:
2412:
2407:
2398:
2393:
2388:
2382:
2373:
2368:
2359:
2350:
2345:
2340:
2334:
2329:
2324:
2319:
2314:
2309:
2304:
2298:
2296:
2293:
2292:
2291:
2277:
2257:
2235:
2213:
2210:
2158:
2155:
2133:
2130:
2118:Daniel Quillen
2091:Pierre Deligne
2031:
2028:
2020:Michael Atiyah
1996:generalization
1963:
1960:
1937:
1934:
1930:par excellence
1922:Michel Raynaud
1916:Here the term
1914:
1913:
1906:
1896:
1891:
1881:
1874:
1864:
1855:
1850:
1845:
1841:relation with
1832:
1829:six operations
1817:
1815:nuclear spaces
1799:
1796:
1792:Pierre Deligne
1723:
1710:
1658:generic points
1611:coherent sheaf
1534:nuclear spaces
1518:Jean Dieudonné
1505:
1502:
1478:
1475:
1451:Weimar Germany
1446:
1443:
1404:dandelion soup
1398:
1395:
1355:Crafoord Prize
1249:noncommutative
1237:External links
1233:Daniel Quillen
1189:
1186:
1130:une cage dorée
1118:Pierre Cartier
1077:
1074:
954:
951:
947:C.P. Ramanujam
899:Pierre Deligne
887:Michel Raynaud
859:Jean Dieudonné
850:
847:
794:Roger Godement
710:Jean Dieudonné
688:'s Seminar at
670:
667:
594:
591:
550:, came from a
544:Hasidic Jewish
527:
524:
522:
519:
374:
373:
370:
369:
367:
366:
361:
356:
354:Michel Raynaud
351:
346:
341:
336:
334:Pierre Gabriel
331:
326:
324:Pierre Deligne
321:
315:
313:
309:
308:
306:
305:
303:Jean Dieudonné
300:
294:
292:
286:
285:
274:
268:
267:
265:
264:
259:
254:
245:
243:
239:
238:
221:
217:
216:
210:
209:
207:
206:
201:Crafoord Prize
194:
185:
175:
173:
169:
168:
150:
149:Known for
146:
145:
143:
142:
137:
131:
129:
125:
124:
122:
121:
115:
111:
109:
105:
104:
94:
91:(aged 86)
84:
80:
79:
66:
55:
51:
50:
47:
39:
38:
35:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6420:
6409:
6406:
6404:
6401:
6399:
6396:
6394:
6391:
6389:
6386:
6384:
6381:
6379:
6376:
6374:
6371:
6369:
6366:
6364:
6361:
6359:
6356:
6354:
6351:
6349:
6346:
6344:
6341:
6339:
6336:
6335:
6333:
6318:
6314:
6310:
6308:
6300:
6299:
6296:
6286:
6283:
6281:
6278:
6276:
6273:
6271:
6270:Duminil-Copin
6267:
6266:
6264:
6259:
6256:
6254:
6251:
6249:
6246:
6244:
6240:
6239:
6237:
6232:
6229:
6227:
6224:
6222:
6219:
6217:
6213:
6212:
6210:
6205:
6202:
6200:
6197:
6195:
6192:
6190:
6189:Lindenstrauss
6186:
6185:
6183:
6178:
6175:
6173:
6170:
6168:
6165:
6163:
6159:
6158:
6156:
6151:
6148:
6146:
6142:
6141:
6139:
6134:
6131:
6129:
6126:
6124:
6121:
6119:
6115:
6114:
6112:
6107:
6104:
6102:
6099:
6097:
6094:
6092:
6088:
6087:
6085:
6080:
6077:
6075:
6072:
6070:
6067:
6065:
6061:
6060:
6058:
6053:
6050:
6048:
6045:
6043:
6039:
6038:
6036:
6031:
6028:
6026:
6023:
6021:
6017:
6016:
6014:
6009:
6006:
6004:
6001:
5999:
5996:
5994:
5990:
5989:
5987:
5982:
5979:
5977:
5973:
5972:
5970:
5965:
5962:
5960:
5957:
5955:
5952:
5950:
5946:
5945:
5943:
5938:
5935:
5933:
5930:
5928:
5925:
5923:
5919:
5918:
5916:
5911:
5908:
5906:
5902:
5901:
5899:
5894:
5891:
5889:
5885:
5884:
5882:
5877:
5874:
5872:
5868:
5867:
5865:
5860:
5857:
5855:
5851:
5850:
5848:
5843:
5840:
5838:
5834:
5833:
5831:
5830:
5826:
5822:
5815:
5810:
5808:
5803:
5801:
5796:
5795:
5792:
5786:
5783:
5781:
5778:
5776:
5773:
5770:
5768:
5765:
5762:
5759:
5756:
5753:
5750:
5746:
5743:
5739:
5737:
5734:
5732:
5728:
5727:David Mumford
5724:
5721:
5718:
5715:
5713:
5710:
5707:
5704:
5701:
5698:
5696:
5693:
5690:
5686:
5682:
5679:
5676:
5673:
5670:
5667:
5665:
5661:
5658:
5655:
5651:
5650:
5645:
5641:
5636:
5633:
5630:
5629:
5625:
5618:
5614:
5610:
5606:
5602:
5598:
5594:
5590:
5583:
5578:
5575:
5569:
5565:
5560:
5555:
5549:
5541:
5536:
5531:
5526:
5515:
5511:
5507:
5503:
5499:
5495:
5491:
5487:
5486:
5478:
5473:
5466:
5462:
5458:
5452:
5445:
5440:
5435:
5431:
5427:
5421:
5417:
5412:
5411:
5408:
5407:
5401:
5397:
5391:
5387:
5383:
5382:
5377:
5376:Ruelle, David
5373:
5368:
5363:
5359:
5355:
5353:
5347:
5343:
5332:
5328:
5324:
5319:
5312:
5308:
5301:
5296:
5292:
5288:
5281:
5276:
5272:
5268:
5261:
5256:
5252:
5246:
5242:
5241:
5235:
5228:
5221:
5220:
5214:
5210:
5204:
5200:
5196:
5191:
5179:
5174:
5170:
5163:
5159:
5155:
5151:
5145:
5141:
5136:
5130:
5126:
5122:
5121:
5118:
5112:
5108:
5107:
5102:
5098:
5094:
5090:
5086:
5082:
5078:
5069:
5064:
5063:
5057:
5053:
5046:
5042:
5038:
5033:
5026:
5021:
5017:
5013:
5012:
5004:
5000:
4996:
4995:
4992:
4991:
4986:
4982:
4975:
4970:
4965:
4961:
4957:
4956:
4948:
4944:
4940:
4939:David Mumford
4936:
4935:Allyn Jackson
4932:
4931:Michael Artin
4928:
4921:
4916:
4911:
4907:
4903:
4902:
4894:
4890:
4886:
4885:David Mumford
4882:
4881:Allyn Jackson
4878:
4877:Michael Artin
4874:
4873:
4868:
4852:
4848:
4842:
4839:
4834:
4828:
4820:
4814:
4810:
4803:
4800:
4788:
4784:
4778:
4775:
4763:
4759:
4753:
4750:
4745:
4739:
4735:
4734:
4726:
4723:
4718:
4711:
4708:
4703:
4702:
4694:
4691:
4686:
4680:
4676:
4675:
4667:
4664:
4659:
4652:
4649:
4643:
4640:
4635:
4629:
4625:
4624:
4616:
4613:
4608:
4602:
4598:
4597:
4589:
4586:
4582:
4578:
4574:
4568:
4564:
4560:
4559:
4554:
4548:
4546:
4542:
4537:
4531:
4527:
4522:
4521:
4512:
4509:
4504:
4498:
4494:
4493:
4485:
4482:
4477:
4475:0-387-97710-4
4471:
4467:
4463:
4462:Ieke Moerdijk
4459:
4453:
4451:
4447:
4444:, p. 22.
4443:
4438:
4435:
4427:
4423:
4419:
4412:
4405:
4402:
4399:, p. 21.
4398:
4393:
4390:
4386:
4381:
4378:
4374:
4370:
4366:
4359:
4356:
4340:
4333:
4329:
4323:
4320:
4316:
4311:
4308:
4304:
4299:
4296:
4292:
4287:
4284:
4279:
4275:
4269:
4266:
4262:
4258:
4252:
4250:
4246:
4233:
4229:
4223:
4220:
4207:
4203:
4197:
4194:
4181:
4177:
4171:
4168:
4163:
4159:
4152:
4149:
4136:
4132:
4131:The Spectator
4128:
4124:
4118:
4115:
4110:
4108:9780309164801
4104:
4100:
4099:
4094:
4088:
4085:
4080:
4076:
4069:
4066:
4061:
4057:
4051:
4048:
4042:
4037:
4034:
4028:
4023:
4020:
4016:
4011:
4008:
4000:
3999:
3991:
3988:
3984:
3983:Scharlau 2008
3979:
3976:
3960:
3953:
3946:
3943:
3927:
3920:
3914:
3911:
3899:
3895:
3889:
3886:
3882:(in Spanish).
3881:
3875:
3872:
3867:
3863:
3856:
3853:
3848:
3844:
3837:
3834:
3829:
3825:
3818:
3815:
3810:
3806:
3799:
3796:
3780:
3773:
3766:
3763:
3751:
3744:
3741:
3726:
3720:
3717:
3712:
3706:
3703:
3687:
3680:
3677:
3673:
3668:
3665:
3662:
3658:
3652:
3650:
3646:
3642:
3637:
3635:
3633:
3631:
3629:
3627:
3623:
3619:(3): 329â337.
3618:
3614:
3607:
3600:
3598:
3594:
3588:
3585:
3581:
3580:
3575:
3570:
3567:
3559:
3555:
3551:
3547:
3541:
3537:
3533:
3529:
3522:
3518:
3512:
3509:
3504:
3497:
3495:
3491:
3486:
3482:
3475:
3472:
3467:
3460:
3454:
3451:
3447:
3442:
3440:
3436:
3432:
3428:
3424:
3420:
3415:
3410:
3406:
3402:
3401:
3396:
3390:
3387:
3383:
3378:
3375:
3371:
3366:
3363:
3355:
3350:
3345:
3341:
3337:
3330:
3323:
3320:
3317:, "Foreword".
3316:
3311:
3309:
3305:
3299:
3294:
3287:
3284:
3279:
3275:
3268:
3265:
3252:
3248:
3242:
3240:
3236:
3232:
3228:
3223:
3220:
3216:
3215:
3208:
3206:
3202:
3198:
3197:
3190:
3187:
3183:
3182:
3175:
3173:
3171:
3169:
3165:
3161:
3156:
3153:
3149:
3148:Scharlau n.d.
3144:
3141:
3137:
3136:Scharlau 2008
3132:
3129:
3124:
3123:
3118:
3111:
3108:
3104:
3103:Jackson 2004a
3099:
3097:
3095:
3093:
3091:
3089:
3087:
3085:
3083:
3081:
3077:
3064:
3060:
3054:
3052:
3048:
3044:
3039:
3037:
3033:
3030:, p. 40.
3029:
3024:
3021:
3013:
3006:
2999:
2996:
2983:
2979:
2978:mathunion.org
2975:
2969:
2966:
2962:
2958:
2953:
2951:
2949:
2945:
2940:
2939:
2934:
2928:
2925:
2920:
2916:
2912:
2908:
2903:
2898:
2894:
2890:
2887:(7534): 272.
2886:
2882:
2878:
2874:
2870:
2864:
2861:
2855:
2850:
2846:
2839:
2837:
2835:
2831:
2827:
2826:Jackson 2004b
2822:
2820:
2818:
2816:
2814:
2812:
2808:
2804:
2803:Kleinert 2007
2799:
2797:
2795:
2791:
2787:
2782:
2780:
2776:
2772:
2767:
2765:
2763:
2759:
2755:
2750:
2748:
2746:
2744:
2742:
2740:
2736:
2732:
2728:
2723:
2720:
2716:
2715:Scharlau 2008
2711:
2709:
2707:
2705:
2703:
2701:
2699:
2697:
2695:
2691:
2684:
2676:
2672:
2671:Floris Takens
2668:
2664:
2658:
2655:
2651:
2648:Testimony by
2645:
2642:
2635:
2630:
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2597:
2595:
2592:
2590:
2587:
2585:
2582:
2580:
2577:
2575:
2572:
2570:
2567:
2565:
2562:
2559:
2556:
2554:
2551:
2549:
2546:
2543:
2540:
2534:
2531:
2529:
2526:
2524:
2521:
2519:
2518:Nuclear space
2516:
2514:
2511:
2508:
2505:
2499:
2498:Moduli scheme
2496:
2494:
2491:
2488:
2485:
2483:
2480:
2474:
2471:
2469:
2466:
2464:
2461:
2459:
2456:
2453:
2450:
2447:
2444:
2442:
2439:
2437:
2434:
2432:
2429:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2402:
2399:
2397:
2394:
2392:
2389:
2386:
2383:
2377:
2374:
2372:
2371:Delta-functor
2369:
2363:
2360:
2354:
2351:
2349:
2346:
2344:
2341:
2338:
2335:
2333:
2330:
2328:
2325:
2323:
2320:
2318:
2315:
2313:
2310:
2308:
2305:
2303:
2300:
2299:
2294:
2288:
2284:
2280:
2274:
2269:
2268:
2262:
2258:
2254:
2250:
2246:
2242:
2238:
2232:
2228:
2225:(in French).
2224:
2220:
2216:
2215:
2211:
2209:
2207:
2206:
2201:
2200:
2199:The Passenger
2195:
2190:
2189:
2185:
2181:
2177:
2172:
2169:
2167:
2166:Colonel Tears
2163:
2156:
2154:
2152:
2148:
2143:
2139:
2131:
2129:
2127:
2123:
2122:Chern classes
2119:
2115:
2111:
2107:
2103:
2098:
2096:
2092:
2088:
2084:
2080:
2076:
2072:
2067:
2065:
2061:
2057:
2053:
2049:
2045:
2041:
2037:
2029:
2027:
2025:
2021:
2017:
2013:
2009:
2005:
2001:
1997:
1992:
1989:
1985:
1981:
1976:
1974:
1970:
1961:
1959:
1954:
1949:
1947:
1943:
1942:David Mumford
1935:
1933:
1931:
1925:
1923:
1919:
1911:
1907:
1905:
1901:
1897:
1895:
1894:Tame topology
1892:
1890:
1886:
1882:
1879:
1876:Crystals and
1875:
1872:
1868:
1865:
1863:
1859:
1856:
1854:
1851:
1849:
1846:
1844:
1840:
1837:
1833:
1830:
1826:
1822:
1818:
1816:
1812:
1809:
1808:
1807:
1805:
1797:
1795:
1793:
1789:
1784:
1782:
1778:
1774:
1770:
1766:
1761:
1759:
1755:
1751:
1750:
1745:
1741:
1740:
1735:
1731:
1730:
1722:
1718:
1714:
1711:
1709:
1707:
1703:
1697:
1695:
1691:
1687:
1686:Galois theory
1683:
1682:number theory
1679:
1675:
1671:
1670:infinitesimal
1667:
1663:
1659:
1654:
1652:
1648:
1643:
1639:
1635:
1631:
1627:
1623:
1618:
1616:
1612:
1608:
1604:
1603:
1598:
1594:
1589:
1587:
1583:
1579:
1575:
1571:
1567:
1563:
1559:
1555:
1550:
1548:
1543:
1539:
1535:
1531:
1527:
1523:
1519:
1515:
1511:
1503:
1501:
1499:
1495:
1490:
1488:
1484:
1476:
1474:
1472:
1468:
1464:
1460:
1456:
1452:
1444:
1442:
1440:
1436:
1431:
1429:
1424:
1422:
1418:
1413:
1412:Pierre Lochak
1409:
1408:Leila Schneps
1405:
1396:
1394:
1390:
1388:
1383:
1381:
1376:
1372:
1367:
1363:
1359:
1356:
1351:
1349:
1344:
1339:
1335:
1334:Leila Schneps
1331:
1327:
1322:
1320:
1316:
1312:
1307:
1305:
1304:
1299:
1295:
1291:
1287:
1283:
1282:
1276:
1274:
1270:
1266:
1262:
1258:
1254:
1250:
1246:
1242:
1238:
1234:
1230:
1229:
1224:
1220:
1215:
1213:
1209:
1208:
1203:
1199:
1194:
1187:
1185:
1183:
1178:
1174:
1169:
1167:
1163:
1159:
1158:Pierre Samuel
1155:
1150:
1148:
1144:
1140:
1135:
1131:
1127:
1123:
1119:
1114:
1112:
1107:
1103:
1099:
1095:
1091:
1087:
1083:
1075:
1073:
1071:
1067:
1066:
1061:
1056:
1054:
1050:
1046:
1042:
1038:
1034:
1033:Galois theory
1030:
1026:
1022:
1018:
1015:, as well as
1014:
1010:
1006:
1002:
1001:
996:
992:
988:
984:
980:
976:
972:
968:
964:
963:number theory
960:
952:
950:
948:
944:
940:
936:
935:David Mumford
932:
928:
924:
920:
916:
912:
908:
904:
903:Michael Artin
900:
897:theory), and
896:
892:
888:
884:
880:
879:group schemes
876:
871:
869:
864:
860:
856:
848:
846:
844:
840:
836:
830:
825:
823:
822:Leila Schneps
819:
815:
811:
810:Yvonne Bruhat
807:
803:
799:
795:
791:
790:Pierre Samuel
785:
778:
776:
775:Oscar Zariski
772:
767:
765:
761:
757:
753:
749:
745:
740:
738:
737:Banach spaces
734:
730:
726:
721:
719:
715:
711:
707:
703:
699:
693:
687:
682:
680:
676:
668:
666:
664:
659:
657:
652:
650:
646:
642:
638:
633:
631:
627:
622:
620:
616:
612:
608:
604:
603:Rieucros Camp
600:
592:
590:
588:
584:
580:
576:
573:
569:
565:
560:
557:
553:
549:
545:
541:
537:
533:
525:
520:
518:
516:
512:
507:
503:
499:
495:
491:
487:
482:
480:
476:
472:
468:
464:
460:
456:
452:
451:mathematician
447:
436:
430:
420:
384:
380:
371:
365:
362:
360:
357:
355:
352:
350:
347:
345:
342:
340:
337:
335:
332:
330:
327:
325:
322:
320:
317:
316:
314:
310:
304:
301:
299:
296:
295:
293:
291:
287:
280:
279:
275:
273:
269:
263:
260:
258:
255:
252:
251:scientifiques
247:
246:
244:
240:
237:
233:
229:
225:
222:
218:
215:
211:
202:
195:
193:
186:
184:
177:
176:
174:
170:
167:
163:
159:
158:number theory
155:
151:
147:
141:
138:
136:
133:
132:
130:
126:
119:
116:
113:
112:
110:
106:
101:
97:
85:
81:
77:
73:
69:
64:28 March 1928
56:
52:
45:
40:
33:
30:
19:
5932:Grothendieck
5931:
5647:
5592:
5588:
5563:
5517:. Retrieved
5489:
5483:
5456:
5415:
5405:
5380:
5357:
5351:
5335:, retrieved
5331:the original
5327:Science News
5326:
5306:
5290:
5286:
5270:
5266:
5239:
5227:the original
5218:
5194:
5182:. Retrieved
5168:
5139:
5105:
5085:Illusie, Luc
5056:the original
5051:
5015:
5009:
4989:
4959:
4953:
4905:
4899:
4854:. Retrieved
4851:The Atlantic
4850:
4841:
4808:
4802:
4790:. Retrieved
4786:
4777:
4767:12 September
4765:. Retrieved
4761:
4752:
4732:
4725:
4716:
4710:
4700:
4693:
4673:
4666:
4657:
4651:
4642:
4622:
4615:
4595:
4588:
4556:
4519:
4511:
4491:
4484:
4465:
4437:
4426:the original
4421:
4417:
4404:
4392:
4380:
4372:
4368:
4358:
4346:. Retrieved
4322:
4315:Deligne 1998
4310:
4298:
4286:
4278:the original
4268:
4261:The Guardian
4236:. Retrieved
4232:the original
4222:
4210:. Retrieved
4196:
4186:12 September
4184:. Retrieved
4179:
4170:
4164:(in French).
4161:
4151:
4139:. Retrieved
4135:the original
4130:
4117:
4097:
4087:
4078:
4068:
4062:(in French).
4059:
4050:
4036:
4022:
4010:
3997:
3990:
3978:
3966:. Retrieved
3945:
3933:. Retrieved
3926:the original
3913:
3903:12 September
3901:. Retrieved
3898:www.mccme.ru
3897:
3888:
3874:
3865:
3861:
3855:
3846:
3842:
3836:
3827:
3823:
3817:
3808:
3804:
3798:
3786:. Retrieved
3765:
3753:. Retrieved
3748:Roy Lisker.
3743:
3733:15 September
3731:. Retrieved
3719:
3705:
3695:17 September
3693:. Retrieved
3679:
3667:
3641:Pragacz 2005
3616:
3612:
3587:
3577:
3573:
3569:
3527:
3511:
3502:
3484:
3474:
3465:
3453:
3404:
3398:
3394:
3389:
3377:
3365:
3339:
3335:
3322:
3286:
3277:
3267:
3255:. Retrieved
3250:
3222:
3213:
3195:
3189:
3180:
3155:
3143:
3131:
3125:(in French).
3120:
3110:
3067:. Retrieved
3063:the original
3043:Cartier 2001
3023:
2998:
2986:. Retrieved
2977:
2968:
2960:
2936:
2927:
2884:
2880:
2863:
2854:the original
2848:
2786:Cartier 2004
2771:Douroux 2012
2754:Cartier 2004
2722:
2657:
2644:
2312:AB5 category
2266:
2260:
2226:
2222:
2218:
2212:Publications
2205:Stella Maris
2203:
2197:
2191:
2179:
2173:
2170:
2165:
2161:
2160:
2135:
2099:
2068:
2052:topos theory
2033:
1993:
1977:
1965:
1956:
1951:
1939:
1929:
1926:
1917:
1915:
1834:Yoga of the
1803:
1801:
1785:
1777:finite field
1762:
1753:
1747:
1743:
1737:
1733:
1727:
1725:
1720:
1716:
1712:
1698:
1673:
1655:
1642:Armand Borel
1619:
1600:
1590:
1569:
1566:TĂŽhoku paper
1551:
1507:
1491:
1483:tuberculosis
1480:
1471:Algerian War
1448:
1435:Saint-Lizier
1432:
1425:
1400:
1391:
1386:
1384:
1379:
1375:Marthe Robin
1361:
1360:
1352:
1347:
1342:
1329:
1325:
1323:
1314:
1308:
1302:
1290:moduli space
1279:
1277:
1269:Fabien Morel
1260:
1256:
1226:
1219:Ronald Brown
1216:
1205:
1201:
1197:
1195:
1191:
1170:
1165:
1161:
1151:
1139:David Ruelle
1129:
1121:
1115:
1079:
1069:
1063:
1059:
1057:
1004:
998:
956:
953:"Golden Age"
872:
862:
852:
832:
829:mathematics.
827:
779:
768:
764:TĂŽhoku paper
741:
722:
686:Henri Cartan
683:
672:
660:
653:
634:
623:
619:World War II
596:
593:World War II
561:
529:
490:Fields Medal
483:
467:sheaf theory
382:
378:
377:
276:
242:Institutions
213:
183:Fields Medal
96:Saint-Lizier
89:(2014-11-13)
29:
6358:Algebraists
6343:2014 deaths
6338:1928 births
6268:2022
6241:2018
6214:2014
6187:2010
6160:2006
6143:2002
6116:1998
6089:1994
6062:1990
6040:1986
6018:1982
5991:1978
5974:1974
5947:1970
5920:1966
5903:1962
5886:1958
5869:1954
5852:1950
5835:1936
5519:1 September
5500:: 930â941.
5457:zbMATH Open
5180:(in French)
4792:15 November
4719:. Springer.
4369:ScienceLine
4255:Phil Hoad,
4238:12 November
4141:26 December
4044:(in French)
4030:(in French)
4004:(in German)
3691:(in French)
3370:Schneps n.d
3257:14 November
3227:Ruelle 2007
3028:Ruelle 2007
2553:Quot scheme
2348:Chern class
1986:on which a
1973:ring theory
1560:theory and
1445:Citizenship
1428:Luc Illusie
1296:theory and
1134:Vietnam War
1098:Vietnam War
943:Barry Mazur
925:worked out
923:Jean Giraud
883:Luc Illusie
385:in French (
344:Luc Illusie
339:Jean Giraud
224:Mathematics
108:Nationality
6332:Categories
6231:Mirzakhani
6128:Kontsevich
5685:Tim Porter
5465:1129.01018
4856:5 December
4385:Leith 2004
4303:Serre 1955
4212:13 October
4123:Leith, Sam
3968:2 December
3788:25 January
3755:25 January
3298:1605.08112
3229:, p.
2873:Tate, John
2729:, p.
2685:References
2675:turbulence
2302:â-groupoid
2060:set theory
2036:cohomology
1885:derivators
1773:André Weil
1666:nilpotents
1626:Hirzebruch
1597:Jean Leray
1251:theory of
1086:pacifistic
849:IHĂS years
698:André Weil
651:in 1942.
552:Protestant
204:(declined)
60:1928-03-28
6285:Viazovska
6258:Venkatesh
6150:Voevodsky
6145:Lafforgue
6118:Borcherds
6042:Donaldson
5998:Fefferman
5905:Hörmander
5731:John Tate
5506:1088-9477
5434:801767784
5199:Gallimard
4943:John Tate
4889:John Tate
4827:cite book
3423:0040-8735
2988:5 January
2911:0028-0836
2396:DĂ©vissage
2376:Derivator
2008:algebraic
1946:John Tate
1936:Influence
1706:D-modules
1463:stateless
1338:MIT Press
911:Nick Katz
806:Jean Cerf
798:René Thom
599:Le Vernet
566:to evade
536:anarchist
152:Renewing
118:Stateless
6307:Category
6221:Bhargava
6167:Perelman
6162:Okounkov
6133:McMullen
6106:Zelmanov
6091:Bourgain
6064:Drinfeld
6052:Freedman
6047:Faltings
6025:Thurston
6003:Margulis
5976:Bombieri
5964:Thompson
5954:Hironaka
5854:Schwartz
5548:cite web
5514:34550461
5378:(2007).
5337:5 August
5311:archived
5160:(1998),
5043:(2004),
5001:(2001).
4974:Archived
4920:Archived
4555:(1977),
4464:(1992).
4348:29 April
4339:Archived
4206:Archived
4162:Le Monde
4095:(2006).
3959:Archived
3779:Archived
3558:Archived
3519:(2009).
3354:Archived
3122:Le Monde
3012:Archived
2982:Archived
2919:25592527
2875:(2015).
2458:K-theory
2401:DF-space
2295:See also
2263:(1973).
1962:Geometry
1898:Yoga of
1869:and the
1839:K-theory
1607:morphism
1542:L spaces
1494:landlady
1421:Pyrenees
1343:Survivre
1162:Survivre
987:K-theory
967:topology
863:de facto
837:and the
630:pensions
572:Lutheran
515:Pyrenees
511:Lasserre
502:K-theory
381:, later
162:topology
102:, France
6280:Maynard
6253:Scholze
6248:Figalli
6204:Villani
6199:Smirnov
6008:Quillen
5993:Deligne
5981:Mumford
5959:Novikov
5871:Kodaira
5859:Selberg
5842:Douglas
5837:Ahlfors
5662:at the
5617:0068874
5609:1969915
5184:2 April
4787:YouTube
4581:0463157
3935:17 June
3554:2490557
3431:0102537
3069:15 June
2889:Bibcode
2253:1315788
2245:0075539
2102:motives
1980:schemes
1948:wrote:
1867:Motives
1848:Schemes
1821:duality
1662:schemes
1498:commune
1147:Biology
1143:physics
1082:radical
995:schemes
607:Mendel.
579:Hamburg
556:Hamburg
513:in the
442:French:
425:German:
76:Germany
72:Prussia
6243:Birkar
6226:Hairer
6177:Werner
6123:Gowers
6101:Yoccoz
6079:Witten
6020:Connes
5922:Atiyah
5910:Milnor
5729:&
5615:
5607:
5570:
5512:
5504:
5463:
5432:
5422:
5392:
5247:
5205:
5146:
5113:
4815:
4740:
4681:
4630:
4603:
4579:
4569:
4532:
4499:
4472:
4105:
4056:"IMAG"
3552:
3542:
3429:
3421:
2917:
2909:
2881:Nature
2307:λ-ring
2287:886098
2285:
2275:
2251:
2243:
2233:
2112:, and
2046:, and
1736:) and
1628:. The
1547:Banach
1477:Family
1253:stacks
973:, and
927:torsor
917:, and
824:said:
816:, and
611:Hitler
575:pastor
568:Nazism
532:Berlin
500:, and
469:, and
283:(1953)
281:
272:Thesis
253:(IHĂS)
220:Fields
199:
190:
181:
172:Awards
100:AriĂšge
68:Berlin
6216:Avila
6096:Lions
6069:Jones
5949:Baker
5937:Smale
5927:Cohen
5876:Serre
5605:JSTOR
5585:(PDF)
5492:(8).
5480:(PDF)
5447:(PDF)
5314:(PDF)
5303:(PDF)
5283:(PDF)
5263:(PDF)
5230:(PDF)
5223:(PDF)
5165:(PDF)
5071:(PDF)
5059:(PDF)
5048:(PDF)
5006:(PDF)
4977:(PDF)
4950:(PDF)
4923:(PDF)
4896:(PDF)
4429:(PDF)
4414:(PDF)
4342:(PDF)
4335:(PDF)
4002:(PDF)
3962:(PDF)
3955:(PDF)
3929:(PDF)
3922:(PDF)
3864:[
3845:[
3826:[
3807:[
3782:(PDF)
3775:(PDF)
3728:(PDF)
3689:(PDF)
3609:(PDF)
3561:(PDF)
3524:(PDF)
3462:(PDF)
3357:(PDF)
3332:(PDF)
3293:arXiv
3015:(PDF)
3008:(PDF)
2665:in a
2636:Notes
2178:book
1853:Topoi
1765:Ă©tale
1558:sheaf
1514:Nancy
1366:deity
1106:Hanoi
1025:topos
564:Paris
6074:Mori
5893:Thom
5888:Roth
5568:ISBN
5554:link
5521:2011
5510:OCLC
5502:ISSN
5430:OCLC
5420:ISBN
5390:ISBN
5339:2008
5245:ISBN
5203:ISBN
5186:2014
5144:ISBN
5111:ISBN
4858:2022
4833:link
4813:ISBN
4794:2021
4769:2017
4738:ISBN
4679:ISBN
4628:ISBN
4601:ISBN
4567:ISBN
4530:ISBN
4497:ISBN
4470:ISBN
4350:2020
4240:2013
4214:2015
4188:2017
4143:2019
4103:ISBN
3970:2021
3937:2005
3905:2017
3790:2022
3757:2022
3735:2024
3697:2024
3540:ISBN
3419:ISSN
3259:2014
3071:2011
2990:2022
2915:PMID
2907:ISSN
2283:OCLC
2273:ISBN
2249:OCLC
2231:ISBN
2174:The
2069:The
2062:and
2022:and
2010:and
1994:His
1944:and
1918:yoga
1860:and
1813:and
1767:and
1638:Bonn
1520:and
1437:or
1410:and
1385:The
1271:and
1243:and
1182:CNRS
1156:and
1128:as "
1120:, a
1092:and
1084:and
1019:and
945:and
766:".
750:and
712:and
521:Life
197:1988
188:1977
179:1966
160:and
83:Died
54:Born
6275:Huh
6194:NgĂŽ
6172:Tao
6030:Yau
5597:doi
5461:Zbl
5362:doi
5020:doi
4964:doi
4910:doi
4526:115
3532:doi
3409:doi
3344:doi
2897:doi
2885:517
2196:'s
2192:In
1827:, "
1754:FGA
1744:SGA
1734:EGA
1721:FGA
1717:SGA
1713:EGA
1636:in
1568:" (
1528:of
1489:.
1315:EGA
1267:of
1175:at
1070:SGA
1060:EGA
1005:EGA
921:).
909:),
881:),
841:in
820:),
773:by
739:).
665:".
534:to
6334::
5652:,
5646:,
5642:,
5613:MR
5611:.
5603:.
5593:61
5591:.
5587:.
5550:}}
5546:{{
5508:.
5496::
5490:55
5488:.
5482:.
5459:.
5428:.
5388:.
5384:.
5356:.
5348:.
5325:,
5291:51
5289:,
5285:,
5271:51
5269:,
5265:,
5201:.
5167:,
5099:;
5095:;
5091:;
5087:;
5083:;
5016:38
5014:.
5008:.
4972:.
4960:63
4958:.
4952:.
4941:;
4937:;
4933:;
4918:.
4906:63
4904:.
4898:.
4887:;
4883:;
4879:;
4849:.
4829:}}
4825:{{
4785:.
4760:.
4577:MR
4575:,
4561:,
4544:^
4528:.
4460:;
4449:^
4422:50
4420:.
4371:.
4367:.
4337:.
4330:.
4259:,
4248:^
4204:.
4178:.
4129:.
4077:.
3957:.
3896:.
3777:.
3659:,
3648:^
3625:^
3617:46
3615:.
3611:.
3596:^
3576:,
3556:.
3550:MR
3548:.
3538:.
3526:.
3493:^
3464:.
3438:^
3427:MR
3425:,
3417:,
3352:.
3340:82
3338:.
3307:^
3249:.
3238:^
3231:35
3204:^
3167:^
3079:^
3050:^
3035:^
3010:.
2980:.
2976:.
2947:^
2935:.
2913:.
2905:.
2895:.
2883:.
2879:.
2871:;
2847:.
2833:^
2810:^
2793:^
2778:^
2761:^
2738:^
2693:^
2281:.
2247:.
2241:MR
2239:.
2227:16
2108:,
2097:.
2066:.
2042:,
2026:.
1902:,
1831:")
1719:,
1715:,
1688:,
1684:,
1653:.
1549:.
1441:.
1423:.
1275:.
1214:.
1184:.
1145:.
1113:.
969:,
965:,
961:,
941:,
937:,
889:,
845:.
812:,
808:,
804:,
800:,
796:,
792:,
708::
496:,
465:,
461:,
440:;
423:;
413:iË
407:Én
401:oÊ
234:,
230:,
226:â
98:,
74:,
70:,
5813:e
5806:t
5799:v
5747:"
5740:"
5691:.
5619:.
5599::
5556:)
5542:.
5532:.
5523:.
5467:.
5436:.
5398:.
5370:.
5364::
5253:.
5211:.
5188:.
5152:.
5131:.
5119:.
5073:.
5034:.
5028:.
5022::
4966::
4912::
4860:.
4835:)
4821:.
4796:.
4771:.
4746:.
4687:.
4636:.
4609:.
4538:.
4505:.
4478:.
4352:.
4317:.
4305:.
4293:.
4242:.
4216:.
4190:.
4145:.
4111:.
4081:.
4017:.
3972:.
3939:.
3907:.
3792:.
3759:.
3737:.
3713:.
3699:.
3674:.
3643:.
3534::
3411::
3405:9
3384:.
3372:.
3346::
3301:.
3295::
3261:.
3233:.
3105:.
3073:.
3045:.
2992:.
2941:.
2921:.
2899::
2891::
2828:.
2805:.
2773:.
2756:.
2733:.
2731:7
2717:.
2289:.
2255:.
2164:(
1928:"
1823:(
1752:(
1742:(
1732:(
1313:(
1200:(
1068:(
1003:(
913:(
905:(
419:/
416:k
410:d
404:t
398:r
395:ÉĄ
392:Ë
389:/
62:)
58:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.