$p$-Selmer group and modular symbols

Ryotaro Sakamoto

doi:10.4171/dm/x21

JournalsdmVol. 27pp. 1891–1922

$p$ -Selmer group and modular symbols

Ryotaro Sakamoto
Department of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan

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Abstract

We prove that the dimension of the $p$ -Selmer group of an elliptic curve is controlled by certain analytic quantities associated with modular symbols as conjectured by Kurihara.

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Ryotaro Sakamoto, $p$ -Selmer group and modular symbols. Doc. Math. 27 (2022), pp. 1891–1922

DOI 10.4171/DM/X21