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December 2020 On Selmer Groups in the Supersingular Reduction Case
Antonio LEI, Ramdorai SUJATHA
Tokyo J. Math. 43(2): 455-479 (December 2020). DOI: 10.3836/tjm/1502179319

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.

Citation

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Antonio LEI. Ramdorai SUJATHA. "On Selmer Groups in the Supersingular Reduction Case." Tokyo J. Math. 43 (2) 455 - 479, December 2020. https://doi.org/10.3836/tjm/1502179319

Information

Published: December 2020
First available in Project Euclid: 13 October 2020

MathSciNet: MR4185844
Digital Object Identifier: 10.3836/tjm/1502179319

Subjects:
Primary: 11R23
Secondary: 11F11, 11G05

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

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Vol.43 • No. 2 • December 2020
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