Nontrivial elements of Sha explained through K3 surfaces

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dc.creatorLogan, Adam
dc.creatorvan Luijk, Ronald
dc.date2007-06-04
dc.date.accessioned2026-07-07T08:04:08Z
dc.date.available2026-07-07T08:04:08Z
dc.descriptionIn this paper we present a new method to show that a principal homogeneous space of the Jacobian of a curve of genus two is nontrivial. The idea is to exhibit a Brauer-Manin obstruction to the existence of rational points on a quotient of this principal homogeneous space. In an explicit example we apply the method to show that a specific curve has infinitely many quadratic twists whose Jacobians have nontrivial Tate-Shafarevich group.
dc.description37 pages
dc.identifierhttps://arxiv.org/abs/0706.0541
dc.identifierhttp://arxiv.org/abs/0706.0541
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129838
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14H40; 11G10; 14J27-28
dc.titleNontrivial elements of Sha explained through K3 surfaces
dc.typetext

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