Mathematical Research Letters

Volume 16, Issue 3, May 2009 pp. 449-461.

Elliptic curves with large Tate-Shafarevich groups over a number field

Authors: Kazuo Matsuno
Author institution: Tsuda College

Summary: Let $p$ be a prime number and let $K$ be a cyclic Galois extension of $\Q$ of degree $p$. We prove that the $p$-rank of the Tate-Shafarevich group over $K$ of elliptic curves defined over $\Q$ can be arbitrarily large.

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