Translator Disclaimer
June 2018 On the Plus and the Minus Selmer Groups for Elliptic Curves at Supersingular Primes
Takahiro KITAJIMA, Rei OTSUKI
Tokyo J. Math. 41(1): 273-303 (June 2018). DOI: 10.3836/tjm/1502179270

Abstract

Let $p$ be an odd prime number, and $E$ an elliptic curve defined over a number field. Suppose that $E$ has good reduction at any prime lying above $p$, and has supersingular reduction at some prime lying above $p$. In this paper, we construct the plus and the minus Selmer groups of $E$ over the cyclotomic $\mathbb Z_p$-extension in a more general setting than that of B.D. Kim, and give a generalization of a result of B.D. Kim on the triviality of finite $\Lambda$-submodules of the Pontryagin duals of the plus and the minus Selmer groups, where $\Lambda$ is the Iwasawa algebra of the Galois group of the $\mathbb Z_p$-extension.

Citation

Download Citation

Takahiro KITAJIMA. Rei OTSUKI. "On the Plus and the Minus Selmer Groups for Elliptic Curves at Supersingular Primes." Tokyo J. Math. 41 (1) 273 - 303, June 2018. https://doi.org/10.3836/tjm/1502179270

Information

Published: June 2018
First available in Project Euclid: 26 January 2018

zbMATH: 06966869
MathSciNet: MR3830819
Digital Object Identifier: 10.3836/tjm/1502179270

Rights: Copyright © 2018 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
31 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.41 • No. 1 • June 2018
Back to Top