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arXiv · 1407.2465

The structure of Selmer groups of elliptic curves and modular symbols

Masato Kurihara
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Abstract

For an elliptic curve over the rational number field and a prime number $p$, we study the structure of the classical Selmer group of $p$-power torsion points. In our previous paper \cite{Ku6}, assuming the main conjecture and the non-degeneracy of the $p$-adic height pairing, we proved that the structure of the Selmer group with respect to $p$-power torsion points is determined by some analytic elements $\tilde{\delta}_{m}$ defined from modular symbols. In this paper, we do not assume the main conjecture nor the non-degeneracy of the $p$-adic height pairing, and study the structure of Selmer groups, using these analytic elements and Kolyvagin systems of Gauss sum type.

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Masato Kurihara. 2014-07-09. The structure of Selmer groups of elliptic curves and modular symbols. https://arxiv.org/abs/1407.2465

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