Geodesic
Non-existence of points rational over number fields on Shimura curves
Keisuke Arai1
1 Department of Mathematics School of Science and Technology for Future Life Tokyo Denki University 5 Senju Asahi-cho, Adachi-ku Tokyo 120-8551, Japan
Acta Arithmetica, Tome 172 (2016) no. 3, pp. 243-250

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa8071-10-2015
Keywords: jordan rotger vera piquero proved shimura curves have points rational imaginary quadratic fields under certain assumption article extend their results number fields higher degree counterexamples hasse principle shimura curves

Keisuke Arai 1

1 Department of Mathematics School of Science and Technology for Future Life Tokyo Denki University 5 Senju Asahi-cho, Adachi-ku Tokyo 120-8551, Japan 
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Keisuke Arai. Non-existence of points rational over number fields on Shimura curves. Acta Arithmetica, Tome 172 (2016) no. 3, pp. 243-250. doi: 10.4064/aa8071-10-2015

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