On the plus and the minus Selmer groups for elliptic curves at supersingular primes

Let \(p\) be an odd prime number, \(E\) 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...

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Bibliographic Details
Published in:arXiv.org 2016-07
Main Authors: Kitajima, Takahiro, Otsuki, Rei
Format: Article
Language:English
Subjects:
Curves
Number theory
Reduction
Online Access:Get full text
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Summary:Let \(p\) be an odd prime number, \(E\) 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.
ISSN:2331-8422