The structure of Selmer groups for elliptic curves and modular symbols
نویسنده
چکیده
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 [12], 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 δ̃m defined from modular symbols (see Theorem 1.1.1 below). In this paper, we do not assume the main conjecture nor the nondegeneracy 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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