Stable cohomology of groups and algebraic varieties

Research output: Contribution to journalArticle

Abstract

The notion of stable cohomology of algebraic varieties and, based on it, the analogous concept for finite and profinite groups are introduced. It is proved that the ordinary and stable cohomology coincide for the Galois group of the algebraic closure of a function field with an algebraically closed constant field of characteristic zero, and also that the unramified cohomology of this Galois group with coefficients in a module with trivial group action coincides with the unramified cohomology groups of a variety having a given field of rational functions.Bibliography: 9 titles.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalSbornik Mathematics
Volume76
Issue number1
DOIs
StatePublished - Feb 28 1993

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Cohomology of Groups
Algebraic Variety
Cohomology
Galois group
Profinite Groups
Function Fields
Group Action
Algebraically closed
Rational function
Trivial
Closure
Finite Group
Module
Zero
Coefficient

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Stable cohomology of groups and algebraic varieties. / Bogomolov, Fedor.

In: Sbornik Mathematics, Vol. 76, No. 1, 28.02.1993, p. 1-21.

Research output: Contribution to journalArticle

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