| Project/Area Number |
11440003
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | KYOTO UNIVERSITY (2001)
The University of Tokyo (1999-2000) |
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Principal Investigator |
KATO Kazuya Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90111450)
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| Co-Investigator(Kenkyū-buntansha) |
KATURA Toshiyuki Dept Math. Sci. Univ. of Tokyo Professor, 大学院・数理科学研究科, 教授 (40108444)
SAITO Takeshi Dept Math. Sci. Univ. of Tokyo Professor, 大学院・数理科学研究科, 教授 (70201506)
YOSHIDA Hiroyuki Graduate School of Science Professor, 大学院・理学研究科, 教授 (40108973)
ODA Takayuki Dept Math. Sci. Univ. of Tokyo Professor, 大学院・数理科学研究科, 教授 (10109415)
UENO Kenji Graduate School of Science Professor, 大学院・理学研究科, 教授 (40011655)
川又 雄二郎 東京大学, 大学院・数理科学研究科, 教授 (90126037)
寺杣 友秀 東京大学, 大学院・数理科学研究科, 助教授 (50192654)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥10,300,000 (Direct Cost: ¥10,300,000)
Fiscal Year 2001: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2000: ¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 1999: ¥3,400,000 (Direct Cost: ¥3,400,000)
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| Keywords | Harse zeta function / moduler forms / Iwasawa theory / abelian variety / BSD conjecture / conductor / log geometry / Birch Swinnerton-Dyer予想 / Hodge構造 / log代数多様体 / 退化 / 導手公式 / SL(2)-orbit / 代数体 / エタール・コホモロジー / 微分加群 / 対数的アーベル多様体 / コンパクト化 / 極小モデル / ホッジ構造 / リーマン・ヒルベルト対応 |
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| Research Abstract |
Concerning Iwasawa theory of moduar forms, I completed the preprint "p-adic Hoclge theory and values of zeta funcions of moduar forms" (244 pages). In this paper, I proved the half of Iwasawa main conjecture for modular forms. (Half means one 【less than or equal】 in the conjecture which has the form of the equality "zeta side"="arithmetic group side.)
As an application I obtained results on BSD confectures on elliptic curves over rational number field.
Concerning BSD 'cong' for abelian varieties over global fields of poeetre characteristic, I proved it assuming the fimteness of Take-Shaturevich group (with F. Trihen).
I proved Blocn's conductor formula by the joint work with Takeshi Saito, This is related also to Harse zeta functions.
I obtained results on log Hodge theory and on log abelian varieties by using the method of log geometry.
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