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arXiv · 1607.03612

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

Takahiro Kitajima·Rei Otsuki
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Abstract

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.

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Takahiro Kitajima, Rei Otsuki. 2016-07-13. On the plus and the minus Selmer groups for elliptic curves at supersingular primes. https://arxiv.org/abs/1607.03612

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