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Algebraic $K$-theory and etale cohomology
Open accessAbstract
Let F be a prime power, and let X be a separated regular noetherian scheme in which / is invertible.If (9^ contains a primitive Fth root of unity, there is canonical element P in the second algebraic K-group of X with coefficients Z/F, K//; (X), which Bocksteins to the primitive root as an F torsion class in Ki(X).The graded ring K//»(X) may be localized by inverting this P.Under a few mild extra hypotheses on X, the main Theorem 4.1 yields a strongly converging Atiyah-Hirzebruch type spectral sequence that computes K/ft(X) [p~1] in terms of the etale cohomology of X:The result may be reformulated in terms of the etale or topological K-theory of Dwyer and Friedlander as giving an isomorphism between the localized algebraic and topological K-groups as in Theorem 4.11:
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Categories for the Working Mathematician
Lane, S. M. (1971) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-9839-7 · Cited by 8,817
The Geometry of Iterated Loop Spaces
May, J. P. (1972) · Lecture Notes in Mathematics · doi:10.1007/bfb0067491 · Cited by 1,386
Introduction to algebraic K-theory
Milnor, J. (1971) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,281
(1993) · Medical Entomology and Zoology · Cited by 1,116
Categories and cohomology theories
Segal, G. (1974) · Topology · doi:10.1016/0040-9383(74)90022-6 · Cited by 970
Topologie algébrique et théorie des faisceaux
Godement, R. (1964) · Cited by 625
Topological Methods in Algebraic Geometry
Hirzebruch, F. E. P. (1966) · Springer eBooks · doi:10.1007/978-3-642-62018-8 · Cited by 584
On the Cohomology and K-Theory of the General Linear Groups Over a Finite Field
Quillen, D. G. (1972) · Annals of Mathematics · doi:10.2307/1970825 · Cited by 487
$ K$-COHOMOLOGY OF SEVERI-BRAUER VARIETIES AND THE NORM RESIDUE HOMOMORPHISM
Merkur'ev, A. S., & Suslin, A. A. (1983) · Mathematics of the USSR-Izvestiya · doi:10.1070/im1983v021n02abeh001793 · Cited by 450
Relations between K2 and Galois cohomology
Tate, J. (1976) · Inventiones Mathematicae · doi:10.1007/bf01390012 · Cited by 437
Metadata
- Authors
- Thomason, R. W.
- Venue
- Annales scientifiques de l'École normale supérieure
- Publisher
- Societe Mathematique de France
- Published
- 1985
- Volume
- 18
- Issue
- 3
- Pages
- 437-552
- ISSN
- 0012-9593 (ISSN-L)
- 1873-2151
- OpenAlex
- W2136058159
- Cited by
- 301
- References
- 30
- FWCI
- 4.92
- Type
- journal article
- Language
- fr
- Open access
- bronze
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