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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A finiteness theorem in the Galois cohomology of algebraic number fields


Author: Wayne Raskind
Journal: Trans. Amer. Math. Soc. 303 (1987), 743-749
MSC: Primary 11R34; Secondary 14C15, 19E08, 19E15
MathSciNet review: 902795
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Abstract: In this note we show that if $ k$ is an algebraic number field with algebraic closure $ \overline k $ and $ M$ is a finitely generated, free $ {{\mathbf{Z}}_l}$-module with continuous $ \operatorname{Gal} (\overline k /k)$-action, then the continuous Galois cohomology group $ {H^1}(k,\,M)$ is a finitely generated $ {{\mathbf{Z}}_l}$-module under certain conditions on $ M$ (see Theorem 1 below). Also, we present a simpler construction of a mapping due to S. Bloch which relates torsion algebraic cycles and étale cohomology.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0902795-5
Article copyright: © Copyright 1987 American Mathematical Society