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

• Autores: Kazuo Matsuno
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 16, Nº 2-3, 2009, págs. 449-461
• Idioma: inglés
• DOI: 10.4310/mrl.2009.v16.n3.a6
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• Resumen

  • 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.