Kyoto Journal of Mathematics

Surjectivity of the global-to-local map defining a Selmer group

Ralph Greenberg

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This article studies a map from a global Galois cohomology group to a direct sum of quotients of local Galois cohomology groups. The kernel of such a global-to-local map is often called a Selmer group. The objective of this article is to study the cokernel of such a map. We do so in a very general context. In particular, we find various sets of assumptions which imply that a global-to-local map is surjective.

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Kyoto J. Math., Volume 50, Number 4 (2010), 853-888.

First available in Project Euclid: 29 November 2010

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Zentralblatt MATH identifier

Primary: 11R23: Iwasawa theory 11R34: Galois cohomology [See also 12Gxx, 19A31]
Secondary: 11G05: Elliptic curves over global fields [See also 14H52] 11G10: Abelian varieties of dimension > 1 [See also 14Kxx]


Greenberg, Ralph. Surjectivity of the global-to-local map defining a Selmer group. Kyoto J. Math. 50 (2010), no. 4, 853--888. doi:10.1215/0023608X-2010-016.

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