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was a major piece of work in complex differential geometry which settled several important questions of both classical and modern significance. The input from Weil conjectures, Hodge theory, variations of Hodge structures, and many geometric and topological tools were critical to its investigations.
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theory is related, by the idea that such varieties should parametrize not just good (arithmetically interesting) families of Hodge structures, but actual motives. This theory is not yet a finished product, and more recent trends have used
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in 2013, "for seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields". He was elected a foreign member of the
Academie des Sciences de Paris in 1978.
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There is a conjecture named the
Deligne–Milnor conjecture for the differential interpretation of a formula of Milnor for Milnor fibres, as part of the extension of nearby cycles and their Euler numbers.
3009:
3039:
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From 1970 until 1984, Deligne was a permanent member of the IHÉS staff. During this time he did much important work outside of his work on algebraic geometry. In joint work with
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and the old and new estimates of the classical exponential sums, among other applications. Deligne's 1980 paper contains a much more general version of the
Riemann hypothesis.
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1059:
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831:. Vols. 1, 2. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997. Edited by Pierre Deligne,
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859:. American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 1999. Vol. 1: xxii+723 pp.; Vol. 2: pp. i–xxiv and 727–1501.
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576:. Other important research achievements of Deligne include the notion of cohomological descent, motivic L-functions, mixed sheaves, nearby
1198:
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434:, a powerful tool in algebraic geometry that generalizes classical Hodge theory, was created by applying weight filtration, Hironaka's
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of weight greater than one; weight one was proved in his work with Serre. Deligne's 1974 paper contains the first proof of the
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2429:
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644:
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446:– the Tannakian category concept being the categorical expression of the linearity of the theory of motives as the ultimate
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443:
407:
364:
165:
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1218:
1099:
993:
848:
752:
536:
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1315:; Migliorini, Luca (October 2009). "The decomposition theorem, perverse sheaves and the topology of algebraic maps".
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267:(Theorem of Lefschetz and criteria of degeneration of spectral sequences). He completed his doctorate at the
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2006:
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398:, Deligne worked on the moduli spaces from the 'fine' arithmetic point of view, with application to
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In terms of the completion of some of the underlying
Grothendieck program of research, he defined
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588:, providing the modern axiomatic definition of Shimura varieties, the work in collaboration with
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beyond their general format, generating a new method of research in this subject. His paper with
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Deligne wrote multiple hand-written letters to other mathematicians in the 1970s. These include
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The
Deligne–Milne conjecture is formulated as part of motives and Tannakian categories.
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for curves. Their work came to be seen as an introduction to one form of the theory of
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Yakov
Varshavsky (2005), "A proof of a generalization of Deligne's conjecture", p. 1.
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and other methods, which he then used to prove the Weil conjectures. He reworked the
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343:. But Deligne's most famous contribution was his proof of the third and last of the
223:; born 3 October 1944) is a Belgian mathematician. He is best known for work on the
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There is a conjecture named the
Deligne–Grothendieck conjecture for the discrete
728:
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1984:
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585:
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307:; their work led to important results on the l-adic representations attached to
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Additionally, many different conjectures in mathematics have been called the
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503:. It was also used by Deligne himself to greatly clarify the nature of the
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Proceedings of the
International Congress of Mathematicians, Helsinki 1978
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Royal
Swedish Academy of Sciences: Many new members elected to the Academy
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422:, as a surrogate for the missing and still largely conjectural theory of
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lasting for more than a decade. As a corollary he proved the celebrated
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Théorème de
Lefschetz et critères de dégénérescence de suites spectrales
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theory in his 1990 paper for the "Grothendieck Festschrift", employing
347:. This proof completed a programme initiated and largely developed by
323:. He introduced the concept of weights and tested them on objects in
1193:
227:, leading to a complete proof in 1973. He is the winner of the 2013
1602:
907:
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An introduction to his work at the time of his Fields medal award.
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426:. This idea allows one to get around the lack of knowledge of the
272:
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of historical importance in relation with the development of the
495:. This theory plays an important role in the recent proof of the
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1178:(now called Fujiwara's theorem for equivariant correspondences).
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theory (but published in the 80s) on the problem have appeared.
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The following mathematical concepts are named after Deligne:
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and p-adic L-functions form an important part of his work in
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on the examples of non-arithmetic lattices and monodromy of
363:. Deligne's contribution was to supply the estimate of the
339:, and recently has been applied to questions arising from
295:(IHÉS) near Paris, initially on the generalization within
291:
Starting in 1965, Deligne worked with Grothendieck at the
491:, Deligne made definitive contributions to the theory of
733:
Grothendieck Festschrift Vol II. Progress in Mathematics
3030:
Members of the Norwegian Academy of Science and Letters
829:
Quantum fields and strings: a course for mathematicians
3035:
Foreign associates of the National Academy of Sciences
1258:
Abramovich, Dan; Graber, Tom; Vistoli, Angelo (2008).
1008:
908:"Deligne's letter to Jean-Pierre Serre (around 1974)"
639:
In 2009, Deligne was elected a foreign member of the
1488:"Fujiwara's Theorem for Equivariant Correspondences"
1131:, or purity conjecture for the monodromy filtration.
759:(1975). "Real homotopy theory of Kähler manifolds".
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2388:
2311:
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Deligne's conjecture on the Lefschetz trace formula
1060:
Deligne conjecture on special values of L-functions
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86:
78:
53:
34:
3040:Foreign members of the Russian Academy of Sciences
1014:
109:
3025:Members of the Royal Swedish Academy of Sciences
1362:– Belgian Federal Public Service. 18 July 2006
1270:(5). Johns Hopkins University Press: 1337–1398.
1260:"Gromov-Witten Theory of Deligne-Mumford Stacks"
531:In 1974 at the IHÉS, Deligne's joint paper with
511:to higher dimensions. Prior to Deligne's paper,
882:"Deligne's letter to Piatetskii-Shapiro (1973)"
814:. Princeton, N.J.: Princeton University Press.
632:In 2006 he was ennobled by the Belgian king as
568:on abelian L-functions and their extensions to
3010:Free University of Brussels (1834–1969) alumni
2625:
2156:
1618:
1317:Bulletin of the American Mathematical Society
1051:Deligne's conjecture on Hochschild cohomology
8:
1550:'s home page at Institute for Advanced Study
1463:Deligne tensor product of abelian categories
1087:is an integer in some set depending on
1000:Deligne tensor product of abelian categories
812:Commensurabilities among Lattices in PU(1,n)
1557:(June 1980), "The Work of Pierre Deligne",
560:into an algebraic setting and extended the
371:, considered the geometric analogue of the
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2610:
2163:
2149:
2141:
1625:
1611:
1603:
1593:: CS1 maint: location missing publisher (
42:
31:
3020:Members of the French Academy of Sciences
1544:– Biography and extended video interview.
1328:
1007:
1428:Norwegian Academy of Science and Letters
1239:Standard conjectures on algebraic cycles
649:Norwegian Academy of Science and Letters
293:Institut des Hautes Études Scientifiques
170:Institut des Hautes Études Scientifiques
1515:MacTutor History of Mathematics Archive
1250:
430:, for some applications. The theory of
406:in 1978. In 1984, Deligne moved to the
1586:
972:Deligne–Mumford moduli space of curves
916:"Deligne's letter to Looijenga (1974)"
596:in two- and three-dimensional complex
319:. Deligne's also focused on topics in
594:hypergeometric differential equations
263:(ULB), writing a dissertation titled
218:
7:
3015:Institute for Advanced Study faculty
1381:, press release on 12 February 2009
934:"Deligne's letter to Millson (1986)"
700:Publications Mathématiques de l'IHÉS
667:Publications Mathématiques de l'IHÉS
2995:Wolf Prize in Mathematics laureates
2970:21st-century Belgian mathematicians
1540:"Simons Foundation: Pierre Deligne"
25:
1360:Official announcement ennoblement
1063:is a formulation of the hope for
696:"La conjecture de Weil : II"
641:Royal Swedish Academy of Sciences
2593:
2124:
2115:
2114:
1031:Langlands–Deligne local constant
643:and a residential member of the
390:to construct representations of
1264:American Journal of Mathematics
1199:Hodge–de Rham spectral sequence
1096:Deligne conjecture on 1-motives
515:'s 1980 thesis and the work of
303:. In 1968, he also worked with
3050:Paris-Saclay University alumni
3045:Paris-Saclay University people
1229:Riemann–Hilbert correspondence
645:American Philosophical Society
509:Hilbert's twenty-first problem
505:Riemann–Hilbert correspondence
375:. It also led to the proof of
353:Ramanujan–Petersson conjecture
275:1972 under the supervision of
1:
1530:Mathematics Genealogy Project
1339:10.1090/S0273-0979-09-01260-9
1234:Serre's modularity conjecture
261:Université libre de Bruxelles
212:Pierre René, Viscount Deligne
91:Université libre de Bruxelles
1566:, Helsinki, pp. 47–52,
1166:Deligne–Langlands conjecture
960:Brylinski-Deligne extensions
952:Concepts named after Deligne
408:Institute for Advanced Study
377:Lefschetz hyperplane theorem
331:on a new description of the
327:. He also collaborated with
166:Institute for Advanced Study
110:Concepts named after Deligne
1424:"Gruppe 1: Matematiske fag"
1219:Motive (algebraic geometry)
1129:weight monodromy conjecture
584:, geometry and topology of
436:resolution of singularities
3066:
1313:de Cataldo, Mark Andrea A.
1214:Moduli of algebraic curves
1015:{\displaystyle \boxtimes }
663:"La conjecture de Weil: I"
450:. All this is part of the
2648:
2589:
2173:Wolf Prize in Mathematics
2110:
1640:
1209:Kodaira vanishing theorem
1098:arising in the theory of
982:Fourier–Deligne transform
729:"Catégories tannakiennes"
392:finite groups of Lie type
205:
146:
41:
3005:Scientists from Brussels
2711:S. R. Srinivasa Varadhan
1520:University of St Andrews
1111:Gross–Deligne conjecture
762:Inventiones Mathematicae
727:Deligne, Pierre (1990).
694:Deligne, Pierre (1980).
661:Deligne, Pierre (1974).
647:. He is a member of the
580:, central extensions of
570:Hilbert modular surfaces
562:Picard-Lefschetz formula
247:Early life and education
1366:30 October 2007 at the
1189:Brumer–Stark conjecture
279:, with a thesis titled
269:University of Paris-Sud
2975:Belgian mathematicians
2600:Mathematics portal
2323:Ilya Piatetski-Shapiro
1146:exceptional Lie groups
1122:Deligne conjecture on
1115:complex multiplication
1016:
977:Deligne–Mumford stacks
967:Deligne–Lusztig theory
460:Galois representations
432:mixed Hodge structures
369:Frobenius endomorphism
349:Alexander Grothendieck
311:, and the conjectural
301:Zariski's main theorem
277:Alexander Grothendieck
182:Alexander Grothendieck
2533:Jean-François Le Gall
1142:representation theory
1017:
808:Mostow, George Daniel
655:Selected publications
420:absolute Hodge cycles
255:, attended school at
48:Deligne in March 2005
27:Belgian mathematician
3000:Viscounts of Belgium
2990:Abel Prize laureates
2980:Arithmetic geometers
2812:John Forbes Nash Jr.
2450:Phillip A. Griffiths
2288:Friedrich Hirzebruch
1542:. Simons Foundation.
1506:Robertson, Edmund F.
1403:search.amphilsoc.org
1399:"APS Member History"
1385:10 July 2018 at the
1170:Langlands philosophy
1155:in characteristic 0.
1153:Riemann–Roch theorem
1127:, also known as the
1006:
872:Hand-written letters
552:His work in complex
313:functional equations
251:Deligne was born in
2523:Alexander Beilinson
1504:O'Connor, John J.;
910:. 15 December 2012.
775:1975InMat..29..245D
608:He was awarded the
574:arithmetic geometry
481:Alexander Beilinson
259:and studied at the
257:Athénée Adolphe Max
2877:Hillel Furstenberg
2554:Simon K. Donaldson
2481:Michael Aschbacher
2440:Hillel Furstenberg
2130:Mathematics portal
1137:Deligne conjecture
1104:algebraic geometry
1043:Deligne conjecture
1036:Weil-Deligne group
1012:
987:Deligne cohomology
894:on 7 December 2012
783:10.1007/BF01389853
749:Griffiths, Phillip
712:10.1007/BF02684780
679:10.1007/bf02684373
554:singularity theory
440:Tannakian category
386:, Deligne applied
373:Riemann hypothesis
18:Deligne conjecture
2947:
2946:
2658:Jean-Pierre Serre
2607:
2606:
2570:Ingrid Daubechies
2527:Vladimir Drinfeld
2517:Charles Fefferman
2400:Jean-Pierre Serre
2248:Shiing-Shen Chern
2222:Andrey Kolmogorov
2171:Laureates of the
2138:
2137:
1113:in the theory of
1026:Deligne's theorem
853:David R. Morrison
806:Deligne, Pierre;
624:in 2008, and the
598:hyperbolic spaces
533:Phillip Griffiths
497:fundamental lemma
305:Jean-Pierre Serre
209:
208:
188:Doctoral students
148:Scientific career
16:(Redirected from
3057:
2985:Fields Medalists
2935:Michel Talagrand
2882:Grigory Margulis
2853:Robert Langlands
2723:John G. Thompson
2699:Lennart Carleson
2634:
2627:
2620:
2611:
2598:
2597:
2558:Yakov Eliashberg
2454:David B. Mumford
2426:Grigory Margulis
2355:Robert Langlands
2333:John G. Thompson
2329:Lennart Carleson
2298:Alberto CalderĂłn
2268:Samuel Eilenberg
2258:Kunihiko Kodaira
2165:
2158:
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2118:
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1634:Fields Medalists
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1620:
1613:
1604:
1598:
1592:
1584:
1582:
1576:, archived from
1565:
1543:
1538:(19 June 2012).
1536:Roberts, Siobhan
1522:
1510:"Pierre Deligne"
1491:
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1426:(in Norwegian).
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1204:Logarithmic form
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887:. Archived from
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757:Sullivan, Dennis
740:
723:
690:
582:reductive groups
578:vanishing cycles
549:Kähler manifolds
517:Masaki Kashiwara
513:Zoghman Mebkhout
507:, which extends
493:perverse sheaves
485:Joseph Bernstein
475:Perverse sheaves
428:Hodge conjecture
402:. He received a
396:Michael Rapoport
388:Ă©tale cohomology
361:Weil conjectures
345:Weil conjectures
337:algebraic stacks
325:complex geometry
281:Théorie de Hodge
225:Weil conjectures
222:
217:
200:Michael Rapoport
177:Doctoral advisor
106:Perverse sheaves
102:Weil conjectures
67:
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46:
32:
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2923:Luis Caffarelli
2915:
2911:Dennis Sullivan
2903:
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2865:Karen Uhlenbeck
2857:
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2817:Louis Nirenberg
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2776:Endre Szemerédi
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2603:
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2542:
2507:James G. Arthur
2485:Luis Caffarelli
2471:Dennis Sullivan
2459:
2406:Vladimir Arnold
2384:
2319:Ennio De Giorgi
2307:
2238:Hassler Whitney
2206:
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1994:
1967:
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1585:
1583:on 12 July 2012
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1486:Martin Olsson,
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1387:Wayback Machine
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906:
897:
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884:
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841:Lisa C. Jeffrey
837:Daniel S. Freed
822:
805:
745:Deligne, Pierre
743:
726:
693:
660:
657:
606:
545:homotopy theory
541:Dennis Sullivan
529:
477:
464:Shimura variety
458:and the l-adic
452:yoga of weights
448:Weil cohomology
416:
289:
249:
220:[dəliɲ]
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87:Alma mater
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1523:
1499:
1498:External links
1496:
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1323:(4): 535–633.
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849:John W. Morgan
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769:(3): 245–274.
741:
724:
691:
656:
653:
614:Crafoord Prize
605:
602:
528:
525:
476:
473:
444:Beck's theorem
415:
412:
410:in Princeton.
384:George Lusztig
288:
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237:Crafoord Prize
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97:Known for
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64:3 October 1944
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865:0-8218-1198-3
862:
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857:Edward Witten
854:
850:
846:
845:David Kazhdan
842:
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833:Pavel Etingof
830:
827:
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821:0-691-00096-4
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623:
620:in 2004, the
619:
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615:
612:in 1978, the
611:
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590:George Mostow
587:
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400:modular forms
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366:
362:
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357:modular forms
354:
350:
346:
342:
341:string theory
338:
334:
333:moduli spaces
330:
329:David Mumford
326:
322:
318:
314:
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309:modular forms
306:
302:
298:
297:scheme theory
294:
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192:Lê Dũng Tráng
190:
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149:
145:
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107:
103:
100:Proof of the
99:
95:
92:
89:
85:
81:
77:
72:
66:(age 79)
56:
52:
45:
40:
33:
30:
19:
2829:Andrew Wiles
2787:
2728:Jacques Tits
2591:
2501:Peter Sarnak
2445:
2359:Andrew Wiles
2349:JĂĽrgen Moser
2343:Jacques Tits
2272:Atle Selberg
2228:Lars Ahlfors
2218:Henri Cartan
1805:
1745:Grothendieck
1578:the original
1559:
1513:
1482:
1473:
1458:
1443:
1431:. Retrieved
1418:
1406:. Retrieved
1402:
1393:
1374:
1355:
1320:
1316:
1307:
1295:. Retrieved
1267:
1263:
1253:
1175:
1165:
1135:
1128:
1121:
1110:
1095:
1088:
1084:
1076:
1072:
1068:
1065:algebraicity
1058:
1049:
1042:
1040:
999:
991:
955:
940:. Retrieved
922:. Retrieved
896:. Retrieved
889:the original
875:
828:
811:
766:
760:
753:Morgan, John
744:
736:
732:
703:
699:
670:
666:
638:
631:
618:Balzan Prize
610:Fields Medal
607:
586:braid groups
556:generalized
543:on the real
530:
501:Ngô Bảo Châu
478:
471:approaches.
456:Hodge theory
451:
417:
414:Hodge cycles
404:Fields Medal
381:
321:Hodge theory
290:
280:
264:
250:
241:Fields Medal
211:
210:
162:Institutions
147:
140:Fields Medal
130:Balzan Prize
29:
2965:1944 births
2933:2024
2921:2023
2909:2022
2892:2021
2875:2020
2863:2019
2851:2018
2839:2017
2827:2016
2810:2015
2800:Yakov Sinai
2798:2014
2786:2013
2774:2012
2764:John Milnor
2762:2011
2750:2010
2738:2009
2721:2008
2709:2007
2697:2006
2685:2005
2668:2004
2656:2003
2302:John Milnor
2081:2022
2054:2018
2027:2014
2000:2010
1973:2006
1956:2002
1929:1998
1902:1994
1875:1990
1853:1986
1831:1982
1804:1978
1787:1974
1760:1970
1733:1966
1716:1962
1699:1958
1682:1954
1665:1950
1648:1936
1164:There is a
1134:There is a
1120:There is a
1109:There is a
1094:There is a
942:11 November
898:15 December
706:: 137–252.
673:: 273–307.
558:Milnor maps
547:of compact
537:John Morgan
527:Other works
489:Ofer Gabber
365:eigenvalues
317:L-functions
239:, and 1978
157:Mathematics
79:Nationality
2954:Categories
2841:Yves Meyer
2641:Abel Prize
2580:Adi Shamir
2416:Mikio Sato
2396:Raoul Bott
2278:Kiyosi ItĂ´
2252:Paul Erdős
2242:Mark Krein
2201:André Weil
2197:Jean Leray
2044:Mirzakhani
1941:Kontsevich
1555:Katz, Nick
1297:13 January
1245:References
1081:L-function
924:20 January
739:: 111–195.
626:Abel Prize
622:Wolf Prize
454:, uniting
233:Wolf Prize
229:Abel Prize
196:Miles Reid
125:Wolf Prize
120:Abel Prize
60:1944-10-03
2752:John Tate
2687:Peter Lax
2643:laureates
2576:Noga Alon
2442:(2006/07)
2422:(2002/03)
2420:John Tate
2371:(1996/97)
2361:(1995/96)
2351:(1994/95)
2282:Peter Lax
2264:(1984/85)
2262:Hans Lewy
2254:(1983/84)
2098:Viazovska
2071:Venkatesh
1963:Voevodsky
1958:Lafforgue
1931:Borcherds
1855:Donaldson
1811:Fefferman
1718:Hörmander
1347:0273-0979
1330:0712.0349
1284:0002-9327
1276:1080-6377
1124:monodromy
1010:⊠
1002:(denoted
720:189769469
687:123139343
566:Ken Ribet
521:D-modules
253:Etterbeek
73:, Belgium
71:Etterbeek
2120:Category
2034:Bhargava
1980:Perelman
1975:Okounkov
1946:McMullen
1919:Zelmanov
1904:Bourgain
1877:Drinfeld
1865:Freedman
1860:Faltings
1838:Thurston
1816:Margulis
1789:Bombieri
1777:Thompson
1767:Hironaka
1667:Schwartz
1589:citation
1433:2 August
1408:23 April
1383:Archived
1364:Archived
1292:40068158
1183:See also
1075:) where
992:Deligne
810:(1993).
634:viscount
519:through
469:K-theory
2093:Maynard
2066:Scholze
2061:Figalli
2017:Villani
2012:Smirnov
1821:Quillen
1806:Deligne
1794:Mumford
1772:Novikov
1684:Kodaira
1672:Selberg
1655:Douglas
1650:Ahlfors
1528:at the
1490:, p. 1.
1140:in the
1100:motives
799:1357812
791:0382702
771:Bibcode
600:, etc.
424:motives
394:; with
367:of the
235:, 1988
231:, 2008
216:French:
122:(2013)
82:Belgian
2582:(2024)
2572:(2023)
2566:(2022)
2560:(2020)
2539:(2019)
2529:(2018)
2519:(2017)
2509:(2015)
2503:(2014)
2497:(2013)
2487:(2012)
2477:(2010)
2456:(2008)
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2412:(2001)
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2345:(1993)
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2203:(1979)
2193:(1978)
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1990:Werner
1936:Gowers
1914:Yoccoz
1892:Witten
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1723:Milnor
1570:
1448:motive
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1079:is an
994:motive
863:
818:
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789:
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604:Awards
487:, and
462:. The
287:Career
154:Fields
142:(1978)
137:(1988)
132:(2004)
127:(2008)
116:Awards
2547:2020s
2464:2010s
2389:2000s
2312:1990s
2211:1980s
2180:1970s
2029:Avila
1909:Lions
1882:Jones
1762:Baker
1750:Smale
1740:Cohen
1689:Serre
1581:(PDF)
1564:(PDF)
1325:arXiv
1288:JSTOR
1272:eISSN
937:(PDF)
919:(PDF)
892:(PDF)
885:(PDF)
795:S2CID
716:S2CID
683:S2CID
479:With
273:Orsay
1887:Mori
1706:Thom
1701:Roth
1595:link
1568:ISBN
1467:nLab
1452:nLab
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1343:ISSN
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