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

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

2007-07-09

arxiv.org/abs/0707.1330v1

Mathematics

Number Theory

25 pages. To appear in Mathematische Annalen

Scientific paper

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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