Abelian Galois Cohomology of Reductive Groups
Author： Mikhail Borovoi
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470402150
P-ISBN(Paperback): 9780821806500
P-ISBN(Hardback): 9780821806500
Subject： O153 Abstract Algebra (modern algebra)
Keyword： Algebra and Algebraic Geometry
Language： ENG
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Abelian Galois Cohomology of Reductive Groups
Description
In this volume, a new functor $H^2_{ab}(K,G)$ of abelian Galois cohomology is introduced from the category of connected reductive groups $G$ over a field $K$ of characteristic $0$ to the category of abelian groups. The abelian Galois cohomology and the abelianization map$ab^1:H^1(K,G) \rightarrow H^2_{ab}(K,G)$ are used to give a functorial, almost explicit description of the usual Galois cohomology set $H^1(K,G)$ when $K$ is a number field.