# Abelian Galois Cohomology of Reductive Groups (Memoirs of the American Mathematical Society No. 626)

By: Mikhail Borovoi (author)Paperback

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### 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.

### Contents

Introduction The algebraic fundamental group of a reductive group Abelian Galois cohomology The abelianization maps Computation of abelian Galois cohomology Galois cohomology over local fields and number fields References.

### Product Details

• publication date: 15/03/1998
• ISBN13: 9780821806500
• Format: Paperback
• Number Of Pages: 50
• ID: 9780821806500
• weight: 142
• ISBN10: 0821806505

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