A finiteness theorem in the Galois cohomology of algebraic number fields
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- by Wayne Raskind PDF
- Trans. Amer. Math. Soc. 303 (1987), 743-749 Request permission
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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 303 (1987), 743-749
- MSC: Primary 11R34; Secondary 14C15, 19E08, 19E15
- DOI: https://doi.org/10.1090/S0002-9947-1987-0902795-5
- MathSciNet review: 902795