Curves over Global Fields Violating the Hasse Principle
نویسنده
چکیده
We exhibit for each global field k an algebraic curve over k which violates the Hasse Principle. We can find such examples among Atkin-Lehner twists of certain elliptic modular curves and Drinfeld modular curves. Our main tool is a refinement of the “Twist Anti-Hasse Principle” (TAHP). We then use TAHP to construct further Hasse Principle violations, e.g. among curves over any number field of any given genus g ≥ 2.
منابع مشابه
Local diophantine properties of modular curves of D-elliptic sheaves
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