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

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.

8 pages

Cited by in corpus (1)

• Points on Shimura curves rational over imaginary quadratic fields in the non-split case