Non-existence of points rational over number fields on Shimura curves
Keisuke Arai
Acta Arithmetica, Tome 172 (2016), p. 243-250 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:279393 
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Keisuke Arai. Non-existence of points rational over number fields on Shimura curves. Acta Arithmetica, Tome 172 (2016) pp. 243-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8071-10-2015/