| eBook ISBN: | 978-1-4704-0215-0 |
| Product Code: | MEMO/132/626.E |
| List Price: | $44.00 |
| MAA Member Price: | $39.60 |
| AMS Member Price: | $26.40 |
| eBook ISBN: | 978-1-4704-0215-0 |
| Product Code: | MEMO/132/626.E |
| List Price: | $44.00 |
| MAA Member Price: | $39.60 |
| AMS Member Price: | $26.40 |
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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.
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Table of Contents
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Chapters
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Introduction
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1. The algebraic fundamental group of a reductive group
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2. Abelian Galois cohomology
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3. The abelianization map
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4. Computation of abelian Galois cohomology
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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
