| 言語種別 | 英語 |
|---|---|
| 発行・発表の年月 | 2018/06 |
| 形態種別 | 学術研究論文 |
| 査読 | 査読あり |
| 標題 | Rational points on Shimura curves and the Manin obstruction |
| 執筆形態 | 単著 |
| 掲載誌名 | Nagoya Mathematical Journal |
| 掲載区分 | 国内 |
| 巻・号・頁 | 230,144-159 |
| 総ページ数 | 16 |
| 概要 | 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. |
| DOI | 10.1017/nmj.2017.6 |