Curves over global fields violating the Hasse Principle

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dc.creatorClark, Pete L.
dc.date2009-05-21
dc.date.accessioned2026-07-07T13:17:08Z
dc.date.available2026-07-07T13:17:08Z
dc.descriptionIn response to a question of B. Poonen, we exhibit for each global field k an algebraic curve over k which violates the Hasse Principle. In fact we can find such examples among Atkin-Lehner twists of certain elliptic modular curves and -- in positive characteristic -- Drinfeld modular curves. Our main tool is a refinement of the "Twist Anti-Hasse Principle" (TAHP). We also use TAHP to construct further Hasse Principle violations, for instance among curves over any number field of any given genus g which is at least 2.
dc.description16 pages; comments welcome
dc.identifierhttps://arxiv.org/abs/0905.3459
dc.identifierhttp://arxiv.org/abs/0905.3459
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231014
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.titleCurves over global fields violating the Hasse Principle
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