Tate Safarevich groups of elliptic curves with complex multiplication

Coates, J.; Liang, Z.; Sujatha, R.

Tate Safarevich groups of elliptic curves with complex multiplication

Authors

Coates, J.

Liang, Z.

Sujatha, R.

Description

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 $p$.