The structure of Selmer groups of elliptic curves and modular symbols

2014/07/09 by Kurihara, Masato
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1407.2465

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 \citeKu6, 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 δ_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.

Related

• The structure of Selmer groups and the Iwasawa main conjecture for elliptic curves
• Selmer groups of twists of elliptic curves over K with K-rational\n torsion points
• p-Selmer group and Modular symbols
• Increasing the p-Selmer rank by twisting
• Kolyvagin systems of rank 0 and the structure of the Selmer group of elliptic curves over abelian extensions