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Abelian Galois Cohomology of Reductive Groups
Mikhail Borovoi, Tel Aviv University, Israel

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
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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.

Table of 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
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