2010 Fiscal Year Final Research Report
Geometry of modular varieties and congruence, P-adic theory of Siegel modular forms
| Project/Area Number |
20540018
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Saga University |
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Principal Investigator |
ICHIKAWA Takashi Saga University, 大学院・工学系研究科, 教授 (20201923)
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| Co-Investigator(Kenkyū-buntansha) |
NAGAOKA SHOUYU 近畿大学, 理工学部, 教授 (20164402)
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| 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)
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| Project Period (FY) |
2008 – 2010
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| Keywords | モジュラー多様体 / モジュラー形式 / 合同 |
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| 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.
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