Non-existence of points rational over number fields on Shimura curves

2014/09/11 by Keisuke Arai, Arai, Keisuke
Mathematics · #11G18 #14G05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G18 #msc:14G05

paper · pdf · doi:10.48550/arxiv.1409.3317

8 pages

arxiv created 2014/09/11 · arxiv updated 2014/09/12

Abstract

Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we expand their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.

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