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

Minhyong Kim

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arXiv · 0710.5290

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

Minhyong Kim

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Abstract

We show how non-vanishing of p-adic L functions controls the dimensions of Selmer varieties associated to the complement of the origin in an elliptic curve with CM. As a corollary, one obtains a π_1-proof of the theorem of Siegel for such curves.

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Minhyong Kim. 2007-10-28. p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication. https://arxiv.org/abs/0710.5290

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