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

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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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Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux, Université de Bordeaux I, 351, cours de la libération, 33 405, Talence Cedex, France

    Pierre Parent

  2. Department of Mathematics, University College London, Gower street, WC1E 6BT, London, UK

    Andrei Yafaev

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  1. Pierre Parent
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  2. Andrei Yafaev
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Correspondence to Pierre Parent.

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Parent, P., Yafaev, A. Proving the triviality of rational points on Atkin–Lehner quotients of Shimura curves. Math. Ann. 339, 915–935 (2007). https://doi.org/10.1007/s00208-007-0136-9

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  • DOI: https://doi.org/10.1007/s00208-007-0136-9

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