Tate Safarevich groups of elliptic curves with complex multiplication

Details Tate Safarevich groups of elliptic curves with complex multiplication Tate Safarevich groups of elliptic curves with complex multiplication

2009-01-24

arxiv.org/abs/0901.3832v1

Mathematics

Number Theory

Scientific paper

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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