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


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.


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