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arXiv · 0901.3832

Tate Safarevich groups of elliptic curves with complex multiplication

J. Coates·Z. Liang·R. Sujatha
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Abstract

We show that the number of copies of ${\Bbb Q}_p/{\Bbb Z}_p$ in the Tate-Shafarevich group of an elliptic curve $E$ over ${\Bbb Q}$ with complex multipication, is at most $2p - g$, where $g$ is the rank of $E({\Bbb Q})$, and for all sufficiently large good ordinary primes $p$.

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J. Coates, Z. Liang, R. Sujatha. 2009-01-24. Tate Safarevich groups of elliptic curves with complex multiplication. https://arxiv.org/abs/0901.3832

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