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arXiv · 2103.06147

On Selmer groups in the supersingular reduction case

Antonio Lei·R. Sujatha
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Abstract

Let $p$ be a fixed odd prime. Let $E$ be an elliptic curve defined over a number field $F$ with good supersingular reduction at all primes above $p$. We study both the classical and plus/minus Selmer groups over the cyclotomic $\mathbb{Z}_p$-extension of $F$. In particular, we give sufficient conditions for these Selmer groups to not contain a non-trivial sub-module of finite index. Furthermore, when $p$ splits completely in $F$, we calculate the Euler characteristics of the plus/minus Selmer groups over the compositum of all $\mathbb{Z}_p$-extensions of $F$ when they are defined.

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Antonio Lei, R. Sujatha. 2021-03-10. On Selmer groups in the supersingular reduction case. https://doi.org/10.3836/tjm%2F1502179319

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