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This article is cited in 43 scientific papers (total in 43 papers)
Cohomology of Severi–Brauer varieties and the norm residue homomorphism
A. S. Merkur'ev, A. A. Suslin
Abstract:
The basic purpose of this paper is to prove bijectivity of the norm residue homomorphism $R_{F,n}\colon K_2(F)/nK_2(F)\to H^2(F,\mu_n^{\otimes 2})$ for any field $F$ of characteristic prime to $n$. In particular, if $\mu_n\subset F$, 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.
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Mathematics of the USSR-Izvestiya, 1983, 21:2, 307–340
Bibliographic databases:
 
UDC:
523.015.7
MSC: Primary 12A62, 14F15, 16A54, 16A61, 16A39; Secondary 13F25, 13A20
Received: 05.04.1982
Citation:
A. S. Merkur'ev, A. A. Suslin, “Cohomology of Severi–Brauer varieties and the norm residue homomorphism”, Izv. Akad. Nauk SSSR Ser. Mat., 46:5 (1982), 1011–1046; Math. USSR-Izv., 21:2 (1983), 307–340
Citation in format AMSBIB
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\by A.~S.~Merkur'ev, A.~A.~Suslin
\paper Cohomology of Severi--Brauer varieties and the norm residue homomorphism
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 5
\pages 1011--1046
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=675529}
\zmath{https://zbmath.org/?q=an:0525.18008}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 2
\pages 307--340
\crossref{https://doi.org/10.1070/IM1983v021n02ABEH001793}
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