206:
269:
643:
752:
89:
80:
580:
Algebraic K-theory, II: Classical algebraic K-theory and connections with arithmetic (Proc. Conf., Battelle
Memorial Inst., Seattle, Wash., 1972)
721:
599:
545:
537:
747:
60:
222:
526:
Grayson, Daniel R. (1994), "Weight filtrations in algebraic K-theory", in
Jannsen, Uwe; Kleiman, Steven;
575:
298:
28:
578:(1973), "Values of zeta-functions, étale cohomology, and algebraic K-theory", in Bass, H. (ed.),
32:
531:
717:
672:
595:
541:
527:
709:
695:
662:
652:
622:
Proceedings of the
International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1
587:
484:
731:
684:
630:
609:
555:
727:
705:
680:
626:
605:
583:
551:
691:
616:
741:
657:
694:(2005), "Algebraic K-theory of rings of integers in local and global fields", in
563:
201:{\displaystyle E_{2}^{pq}=H_{\text{etale}}^{p}({\text{Spec }}A,Z_{\ell }(-q/2)),}
51:
proved the
Quillen–Lichtenbaum conjecture at the prime 2 for some number fields.
56:
20:
676:
713:
52:
699:
638:
667:
591:
639:"Two-primary algebraic K-theory of rings of integers in number fields"
620:
63:, which implies the Quillen–Lichtenbaum conjecture for all primes.
582:, Lecture Notes in Mathematics, vol. 342, Berlin, New York:
79:
is prime, then there is a spectral sequence analogous to the
536:, Proc. Sympos. Pure Math., vol. 55, Providence, R.I.:
625:, Canad. Math. Congress, Montreal, Que., pp. 171–176,
39:, p. 175), who was inspired by earlier conjectures of
71:
The conjecture in
Quillen's original form states that if
75:
is a finitely-generated algebra over the integers and
297:
Assuming the
Quillen–Lichtenbaum conjecture and the
225:
92:
263:
200:
565:The Quillen-Lichtenbaum conjecture at the prime 2
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644:Journal of the American Mathematical Society
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264:{\displaystyle K_{-p-q}A\otimes Z_{\ell }}
666:
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224:
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123:
118:
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282: > 1 + dim
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619:(1975), "Higher algebraic K-theory",
7:
637:Rognes, J.; Weibel, Charles (2000),
44:
81:Atiyah–Hirzebruch spectral sequence
55:, using some important results of
14:
753:Conjectures that have been proved
208:(which is understood to be 0 if
192:
189:
172:
156:
140:
129:
25:Quillen–Lichtenbaum conjecture
1:
698:; Grayson, Daniel R. (eds.),
658:10.1090/S0894-0347-99-00317-3
538:American Mathematical Society
701:Handbook of K-theory. Vol. 1
533:Motives (Seattle, WA, 1991)
769:
49:Rognes & Weibel (2000)
508: − 1 or 4
387: = 2 mod 8
352: = 1 mod 8 and
326: = 0 mod 8 and
305:-groups of the integers,
27:is a conjecture relating
714:10.1007/3-540-27855-9_5
293:-theory of the integers
16:Mathematical conjecture
512: − 2 (
265:
202:
266:
203:
61:Bloch–Kato conjecture
708:, pp. 139–190,
704:, Berlin, New York:
696:Friedlander, Eric M.
586:, pp. 489–501,
576:Lichtenbaum, Stephen
562:Kahn, Bruno (1997),
540:, pp. 207–237,
500:in lowest terms and
461: = 7 mod 8
442: = 6 mod 8
423: = 5 mod 8
413: = 4 mod 8
406: = 3 mod 8
223:
90:
356: > 1,
330: > 0,
299:Vandiver conjecture
278: −
128:
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748:Algebraic K-theory
592:10.1007/BFb0073737
528:Serre, Jean-Pierre
261:
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33:algebraic K-theory
723:978-3-540-23019-9
601:978-3-540-06435-0
547:978-0-8218-1636-3
318:), are given by:
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760:
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570:
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485:Bernoulli number
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268:
267:
262:
260:
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692:Weibel, Charles
690:
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651:(1): 1–54,
514:Weibel 2005
274:for −
57:Markus Rost
45:Kahn (1997)
21:mathematics
742:Categories
520:References
134:Spec
677:0894-0347
257:ℓ
249:⊗
238:−
232:−
176:−
168:ℓ
149:−
145:ℓ
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