| Project/Area Number |
12640038
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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 | Gakushuin University |
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Principal Investigator |
NAKAJIMA Shoichi Gakushuin Univ., Fac.of Sci., Professor, 理学部, 教授 (90172311)
|
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| Co-Investigator(Kenkyū-buntansha) |
ICHIMURA Humio Yokohama City Univ., Fac.of Sci., Professor, 理学部, 教授 (00203109)
NAITO Hirotada Kagawa Univ., Fac.of Education, Professor, 教育学部, 教授 (00180224)
NAKANO Shin Gakushuin Univ., Fac.of Sci., Associate Professor, 理学部, 助教授 (40180327)
KAWAMOTO Fuminori Gakushuin Univ., Fac.of Sci., Assistant, 理学部, 助手 (50195161)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2001: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Iwasawa Theory / Formal Group / Elliptic Curve / 岩澤理論(Iwasawa Theory) / 形式群(Formal Group) / 形式群(Formal Grorp) / 岩澤理論 |
|---|
| Research Abstract |
Iwasawa Theory started as a method for investigating (a tower of) cyclotomic fields and soon was generalized to arbitrary number fields. Recently, Iwasawa Theory for elliptic curves has been constructed and has developed extensively. Iwasawa Theory for number fields is related to multiplicative group and Iwasawa Theory for elliptic curves is naturally related to the group structure of elliptic curves. Our aim in this project was to generalize Iwasawa Theory for formal groups, which include multiplicative and elliptic curve groups as special cases. For that purpose, we first investigated
(1) general theory of formal groups
and, as important examples of the theory,
(2) Iwasawa Theory of number fields (multiplicative group),
(3) Iwasawa Theory of elliptic curves (elliptic curve group).
For (1) we mainly considered Honda's theory which classified formal groups over the integer ring. We also tried numerical computation for formal groups using Maple. For (2) our main concern was Greenberg's conjecture and its relation to normal integral bases. For (3) we obtained results for mu-invariants of elliptic curves, extending the former results of R.Greenberg.
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