eBook ISBN:  9781470402150 
Product Code:  MEMO/132/626.E 
List Price:  $44.00 
MAA Member Price:  $39.60 
AMS Member Price:  $26.40 
eBook ISBN:  9781470402150 
Product Code:  MEMO/132/626.E 
List Price:  $44.00 
MAA Member Price:  $39.60 
AMS Member Price:  $26.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 132; 1998; 50 ppMSC: Primary 20; Secondary 14; 18
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.
ReadershipGraduate students and research mathematicians working in group theory and generalizations.

Table of Contents

Chapters

Introduction

1. The algebraic fundamental group of a reductive group

2. Abelian Galois cohomology

3. The abelianization map

4. Computation of abelian Galois cohomology

5. Galois cohomology over local fields and number fields


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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.
Graduate students and research mathematicians working in group theory and generalizations.

Chapters

Introduction

1. The algebraic fundamental group of a reductive group

2. Abelian Galois cohomology

3. The abelianization map

4. Computation of abelian Galois cohomology

5. Galois cohomology over local fields and number fields