$p$-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