Corpus ID: 18030832

# Selmer groups as flat cohomology groups

@article{Cesnavicius2013SelmerGA,
title={Selmer groups as flat cohomology groups},
author={Kestutis Cesnavicius},
journal={arXiv: Number Theory},
year={2013}
}
Given a prime number $p$, Bloch and Kato showed how the $p^\infty$-Selmer group of an abelian variety $A$ over a number field $K$ is determined by the $p$-adic Tate module. In general, the $p^m$-Selmer group $\mathrm{Sel}_{p^m} A$ need not be determined by the mod $p^m$ Galois representation $A[p^m]$; we show, however, that this is the case if $p$ is large enough. More precisely, we exhibit a finite explicit set of rational primes $\Sigma$ depending on $K$ and $A$, such that \$\mathrm{Sel}_{p^m… Expand
11 Citations
Selmer groups and class groups
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The ℓ-parity conjecture over the constant quadratic extension

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