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

• Autorzy: Keisuke Arai
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11G10: Abelian varieties of dimension > 1
• 11G15: Complex multiplication and moduli of abelian varieties
• 14G05: Rational points
• 11G18: Arithmetic aspects of modular and Shimura varieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 172
• Numer: 3
• Strony: 243-250

Daty

wydano

2016

Twórcy

autor

Keisuke Arai

• Department of Mathematics, School of Science and Technology for Future Life, Tokyo Denki University, 5 Senju Asahi-cho, Adachi-ku, Tokyo 120-8551, Japan

Identyfikatory

DOI

10.4064/aa8071-10-2015