Geometry of modular varieties and congruence, P-adic theory of Siegel modular forms
| Project/Area Number |
20540018
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Saga University |
|---|
Principal Investigator |
ICHIKAWA Takashi Saga University, 大学院・工学系研究科, 教授 (20201923)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NAGAOKA SHOUYU 近畿大学, 理工学部, 教授 (20164402)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
UEHARA Tsuyoshi 佐賀大学, 大学院・工学系研究科, 教授 (80093970)
MIYAZAKI Chikashi 佐賀大学, 大学院・工学系研究科, 教授 (90229831)
TERAI Naoki 佐賀大学, 文化教育学部, 准教授 (90259862)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Project Status |
Completed (Fiscal Year 2010)
|
| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | モジュラー多様体 / モジュラー形式 / 合同 / モジュラー様体 / ジーゲル保型形式 / 保型形式の合同 / P進保型形式 / ベクトル値保型形式 / テータ関数 / ショットキー問題 / ソリトン方程式 / リーマン面 / ベクトル束 / アーベル・ヤコビ写像 / ジーゲル・モジュラー形式 / p進モジュラー形式 / モジュラー曲線 / 志村積分 / アイゼンシュタイン級数 / p進理論 / モノドロミー / 保型形式環 / 数論幾何 / 代数幾何 |
|---|
| Research Abstract |
By studying arithmetic geometry of Siegel modular varieties, we solved the congruence problem of Siegel modular forms, and showed that weights of p-adicSiegel modular forms are determined as p-adic numbers. Further, we constructed a basictheory of arithmetic vector-valued Siegel modular forms and vector-valued p-adic Siegel modular forms with natural p-adic operators. Moreover, we studied the ring structure ofSiegel modular forms over rings in which 6 is invertible, and decided this structure in the degree 2 case.
|
Report
(4 results)
Research Products
(19 results)
