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Abelian Galois Cohomology of Reductive Groups
Mikhail Borovoi, Tel Aviv University, Israel
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Memoirs of the American Mathematical Society
1998; 50 pp; softcover
Volume: 132
ISBN-10: 0-8218-0650-5
ISBN-13: 978-0-8218-0650-0
List Price: US$44 Individual Members: US$26.40
Institutional Members: US\$35.20
Order Code: MEMO/132/626

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.