$p$-adic $L$-functions and Selmer varieties associated to elliptic curves with complex multiplication

Abstract

We show how the finiteness of integral points on an elliptic curve over $\mathbb{Q}$ with complex multiplication can be accounted for by the nonvanishing of $L$-functions that leads to bounds for dimensions of Selmer varieties.

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Authors

Minhyong Kim

Department of Mathematics
University College London
Gower Street
London WC1E 6BT
United Kingdom
and
Korea Institute for Advanced Study
Hoegiro 87
Dongdaemun-gu
Seoul 130-722
Korea