Abstract:
The basic purpose of this paper is to prove bijectivity of the norm residue homomorphism RF,n:K2(F)/nK2(F)→H2(F,μ⊗2n) for any field F of characteristic prime to n. In particular, if μn⊂F, then any central simple algebra of exponent n is similar to a tensor product of cyclic algebras. In the course of the proof we obtain partial degeneracy of the Gersten spectral sequence, and we compute some K-cohomology groups of Severi–Brauer groups corresponding to cyclic algebras of prime degree. The fundamental theorem also gives us several corollaries.
Bibliography: 27 titles.
Citation:
A. S. Merkur'ev, A. A. Suslin, “Cohomology of Severi–Brauer varieties and the norm residue homomorphism”, Math. USSR-Izv., 21:2 (1983), 307–340
\Bibitem{MerSus82}
\by A.~S.~Merkur'ev, A.~A.~Suslin
\paper Cohomology of Severi--Brauer varieties and the norm residue homomorphism
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 2
\pages 307--340
\mathnet{http://mi.mathnet.ru/eng/im1657}
\crossref{https://doi.org/10.1070/IM1983v021n02ABEH001793}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=675529}
\zmath{https://zbmath.org/?q=an:0525.18008}
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https://doi.org/10.1070/IM1983v021n02ABEH001793
https://www.mathnet.ru/eng/im/v46/i5/p1011
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