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arXiv · 1612.01440

Hasse Principle Violations for Atkin-Lehner Twists of Shimura Curves

Pete L. Clark·James Stankewicz
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Abstract

Let $D > 546$ be the discriminant of an indefinite rational quaternion algebra. We show that there are infinitely many imaginary quadratic fields $l/\mathbb Q$ such that the twist of the Shimura curve $X^D$ by the main Atkin-Lehner involution $w_D$ and $l/\mathbb Q$ violates the Hasse Principle over $\mathbb Q$.

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Pete L. Clark, James Stankewicz. 2016-12-05. Hasse Principle Violations for Atkin-Lehner Twists of Shimura Curves. https://arxiv.org/abs/1612.01440

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