# Selmer groups and class groups

@article{Cesnavicius2014SelmerGA,
title={Selmer groups and class groups},
author={Kestutis Cesnavicius},
journal={Compositio Mathematica},
year={2014},
volume={151},
pages={416 - 434}
}
Abstract Let $A$ be an abelian variety over a global field $K$ of characteristic $p\geqslant 0$. If $A$ has nontrivial (respectively full) $K$-rational $l$-torsion for a prime $l\neq p$, we exploit the fppf cohomological interpretation of the $l$-Selmer group $\text{Sel}_{l}\,A$ to bound $\#\text{Sel}_{l}\,A$ from below (respectively above) in terms of the cardinality of the $l$-torsion subgroup of the ideal class group of $K$. Applied over families of finite extensions of $K$, the bounds… Expand
8 Citations
Growth of Fine Selmer Groups in Infinite Towers
p-Selmer growth in extensions of degree p

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