The p-part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large

dc.creatorKloosterman, Remke
dc.date2003-03-12
dc.date2003-05-12
dc.date.accessioned2026-07-07T04:55:58Z
dc.date.available2026-07-07T04:55:58Z
dc.descriptionIn this paper it is shown that for every prime p>5 the dimension of the p-torsion in the Tate-Shafarevich group of E/K can be arbitrarily large, where E is an elliptic curve defined over a number field K, with [K:Q] bounded by a constant depending only on p. From this we deduce that the dimension of the p-torsion in the Tate-Shafarevich group of A/Q can be arbitrarily large, where A is an abelian variety, with dim A bounded by a constant depending only on p.
dc.descriptionSecond version; The final section has been changed to correct a mistake in the first version. Some reference are added
dc.identifierhttps://arxiv.org/abs/math/0303143
dc.identifierhttp://arxiv.org/abs/math/0303143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66765
dc.subjectNumber Theory
dc.subject11G05 (Primary); 11G18 (Secondary)
dc.titleThe p-part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large
dc.typetext

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