Non-existence of points rational over number fields on Shimura curves
Volume 172 / 2016
Acta Arithmetica 172 (2016), 243-250
MSC: Primary 11G18, 14G05; Secondary 11G10, 11G15.
DOI: 10.4064/aa8071-10-2015
Published online: 20 January 2016
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 extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
