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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 5, Pages 1011–1046 (Mi izv1657)  

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.
Bibliography: 27 titles.

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English version:
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
\Bibitem{MerSus82}
\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
\mathnet{http://mi.mathnet.ru/izv1657}
\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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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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