Failure of the Hasse principle for Atkin-Lehner quotients of Shimura curves over \Q

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dc.creatorRotger, V.
dc.creatorSkorobogatov, A.
dc.creatorYafaev, A.
dc.date2004-06-30
dc.date2005-02-22
dc.date.accessioned2026-07-07T05:09:51Z
dc.date.available2026-07-07T05:09:51Z
dc.descriptionWe show how to construct counter-examples to the Hasse principle over the field of rational numbers on Atkin-Lehner quotients of Shimura curves and on twisted forms of Shimura curves by Atkin-Lehner involutions. A particular example is the quotient of the Shimura curve X attached to the indefinite rational quaternion algebra of discriminant 23*107 by the Atkin-Lehner involution w107. The quadratic twist of X by Q(sqrt{-23}) with respect to this involution is also a counter-example to the Hasse principle over Q.
dc.descriptionTo appear in Moscow Math. Journal. Completely revised and improved version
dc.identifierhttps://arxiv.org/abs/math/0406625
dc.identifierhttp://arxiv.org/abs/math/0406625
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71740
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G18 4G35
dc.titleFailure of the Hasse principle for Atkin-Lehner quotients of Shimura curves over \Q
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