K-Cohomology of severi-brauer varieties and the norm residue homomorphism

A. S. Merkur'ev, A. A. Suslin

Research output: Contribution to journalArticlepeer-review

147 Scopus citations

Abstract

The basic purpose of this paper is to prove bijectivity of the norm residue homomorphism for any field of characteristic prime to. In particular, if, then any central simple algebra of exponent 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 -cohomology groups of Severi-Brauer groups corresponding to cyclic algebras of prime degree. The fundamental theorem also gives us several corollaries.Bibliography: 27 titles.

Original languageEnglish (US)
Pages (from-to)307-340
Number of pages34
JournalMathematics of the USSR - Izvestija
Volume21
Issue number2
DOIs
StatePublished - Apr 30 1983

ASJC Scopus subject areas

  • Mathematics(all)

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