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RATIONAL POINTS ON SHIMURA CURVES AND THE MANIN OBSTRUCTION

Published online by Cambridge University Press:  12 April 2017

KEISUKE ARAI*
Affiliation:
Department of Mathematics, School of Science and Technology for Future Life, Tokyo Denki University, 5 Senju Asahi-cho, Adachi-ku, Tokyo 120-8551, Japan email araik@mail.dendai.ac.jp

Abstract

In a previous article, we proved that Shimura curves have no points rational over number fields under a certain assumption. In this article, we give another criterion of the nonexistence of rational points on Shimura curves and obtain new counterexamples to the Hasse principle for Shimura curves. We also prove that such counterexamples obtained from the above results are accounted for by the Manin obstruction.

Type
Article
Copyright
© 2017 by The Editorial Board of the Nagoya Mathematical Journal  

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References

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