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• W1640489932 abstract "In 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 (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." @default.
• W1640489932 created "2016-06-24" @default.
• W1640489932 creator A5049455406 @default.
• W1640489932 date "2009-05-21" @default.
• W1640489932 modified "2023-09-27" @default.
• W1640489932 title "Curves over global fields violating the Hasse Principle" @default.
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• W1640489932 hasPublicationYear "2009" @default.
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