Mathematical Research Letters

Volume 16 (2009)

Number 3

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

Pages: 449 – 461

DOI: https://dx.doi.org/10.4310/MRL.2009.v16.n3.a6

Author

Kazuo Matsuno (Tsuda College)

Abstract

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.

Published 1 January 2009