**Memoirs of the American Mathematical Society**

1998;
50 pp;
Softcover

MSC: Primary 20;
Secondary 14; 18

Print ISBN: 978-0-8218-0650-0

Product Code: MEMO/132/626

List Price: $44.00

AMS Member Price: $26.40

MAA member Price: $39.60

**Electronic ISBN: 978-1-4704-0215-0
Product Code: MEMO/132/626.E**

List Price: $44.00

AMS Member Price: $26.40

MAA member Price: $39.60

# Abelian Galois Cohomology of Reductive Groups

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*Mikhail Borovoi*

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.

#### Readership

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