Mathematical Research Letters

Volume 16 (2009)

Number 3

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

Pages: 449 – 461



Kazuo Matsuno (Tsuda College)


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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