2001 Fiscal Year Final Research Report Summary
Iwasawa theory of Harse zeta functions
| 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)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Harse zeta function / moduler forms / Iwasawa theory / abelian variety / BSD conjecture / conductor / log geometry |
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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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