The effect of twisting on the 2-Selmer group

• Autores: Peter Swinnerton-Dyer
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 3, 2008, págs. 513-526
• Idioma: inglés
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• Resumen

  • Let G be an elliptic curve defined over Q, all of whose 2-division points are rational, and let Gb be its quadratic twist by b. Subject to a mild additional condition on G, we find the limit of the probability distribution of the dimension of the 2-Selmer group of Gb as the number of prime factors of b increases; and we show that this distribution depends only on whether the 2-Selmer group of G has odd or even dimension.