Selmer groups of elliptic curves in degree $p$ extensions

Julio Brau

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arXiv · 1401.3304

Selmer groups of elliptic curves in degree $p$ extensions

Julio Brau

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Abstract

We study the growth of the Galois invariants of the $p$-Selmer group of an elliptic curve in a degree $p$ Galois extension. We show that this growth is determined by certain local cohomology groups and determine necessary and sufficient conditions for these groups to be trivial. Under certain hypotheses this allows us to give necessary and sufficient conditions for there to be growth in the full $p$-Selmer group in a degree $p$ Galois extension.

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BibTeX RIS

Julio Brau. 2014-01-14. Selmer groups of elliptic curves in degree $p$ extensions. https://arxiv.org/abs/1401.3304

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