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arXiv · 0707.1330

Proving the triviality of rational points on Atkin-Lehner quotients of Shimura curves

Pierre Parent·Andrei Yafaev
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Abstract

In this paper we give a method for studying global rational points on certain quotients of Shimura curves by Atkin-Lehner involutions. We obtain explicit conditions on such quotients for rational points to be ``trivial'' (coming from CM points only) and exhibit an explicit infinite family of such quotients satisfying these conditions.

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Pierre Parent, Andrei Yafaev. 2007-07-09. Proving the triviality of rational points on Atkin-Lehner quotients of Shimura curves. https://arxiv.org/abs/0707.1330

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