このアイテムのアクセス数: 382
このアイテムのファイル:
| ファイル | 記述 | サイズ | フォーマット | |
|---|---|---|---|---|
| B83-02.pdf | 147.92 kB | Adobe PDF | 見る/開く |
| タイトル: | 虚数乗法を持つK3曲面の整数論的性質とその応用について (Algebraic Number Theory and Related Topics 2017) |
| その他のタイトル: | On the arithmetic of K3 surfaces with complex multiplication and its applications (Algebraic Number Theory and Related Topics 2017) |
| 著者: | 伊藤, 和広  |
| 著者名の別形: | Ito, Kazuhiro |
| キーワード: | 14J28 14G10 14G15 14K22 K3 surface Hasse-Weil zeta function Complex multiplication Good reduction Tate conjecture |
| 発行日: | Oct-2020 |
| 出版者: | Research Institute for Mathematical Sciences, Kyoto University |
| 誌名: | 数理解析研究所講究録別冊 |
| 巻: | B83 |
| 開始ページ: | 11 |
| 終了ページ: | 26 |
| 抄録: | This survey article is an outline of author's talk at the RIMS Workshop Algebraic Number Theory and Related Topics (2017). We study arithmetic properties of K3 surfaces with complex multiplication (CM) generalizing the results of Shimada for K3 surfaces with Picard number 20. Then, following Taelman's strategy and using Matsumoto's good reduction criterion for K3 surfaces with CM, we construct K3 surfaces over finite fields with given L-function, up to finite extensions of the base fields. We also prove the Tate conjecture for self-products of K3 surfaces over finite fields by CM lifts and the Hodge conjecture for self-products of K3 surfaces with CM proved by Mukai and Buskin. |
| 記述: | Algebraic Number Theory and Related Topics 2017. December 4-8, 2017. edited by Hiroshi Tsunogai, Takao Yamazaki and Yasushi Mizusawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
| 著作権等: | © 2020 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
| URI: | http://hdl.handle.net/2433/260686 |
| 出現コレクション: | B83 Algebraic Number Theory and Related Topics 2017 |
このリポジトリに保管されているアイテムはすべて著作権により保護されています。