Memoirs of the American Mathematical Society 1998; 50 pp; softcover Volume: 132 ISBN10: 0821806505 ISBN13: 9780821806500 List Price: US$41 Individual Members: US$24.60 Institutional Members: US$32.80 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. Readership 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
