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An "Anti-Hasse Principle" for Prime Twists

Pete L. Clark

math.NTarXiv:math/0609465

Abstract

Given an algebraic curve C/Q having points everywhere locally and endowed with a suitable involution, we show that there exists a positive density family of prime quadratic twists of C violating the Hasse principle. The result applies in particular to wN-Atkin-Lehner twists of most modular curves X0(N) and to wp-Atkin-Lehner twists of certain Shimura curves XD+.

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