2013 Fiscal Year Final Research Report
New development of Iwasawa theory and its applications
| Project/Area Number |
21340012
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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 | Keio University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
OTA Katsuhiro 慶應義塾大学, 理工学部, 教授 (40213722)
MATSUNO Kazuo 津田塾大学, 学芸学部, 准教授 (40332936)
HACHIMORI Yoshitaka 東京理科大学, 理工学部, 准教授 (50433743)
BANNAI Kenichi 慶應義塾大学, 理工学部, 准教授 (90343201)
TANAKA Taka-aki 慶應義塾大学, 理工学部, 講師 (60306850)
KOBAYASHI Shinichi 東北大学, 理学(系)研究科, 准教授 (80362226)
MIURA Takashi 慶應義塾大学, 理工学部, 特任助教 (60631934)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 整数論 / セルマー群 / イデアル類群 / 岩澤理論 |
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| Research Abstract |
We studied and obtained a refinement of the usual Iwasawa theory for general p-adic representations. In particular, for an elliptic curve over the rational number field with good ordinary reduction at p, assuming the main conjecture and the non-degeneracy of the p-adic height pairing, we proved a structure theorem for the p-component of the Selmer group of the curve. This theorem describes the structure of the Selmer group as an abelian group by analytic elements which come from modular symbols, so from the L-values. We also constructed a theory of Euler system and Kolyvagin system of Gauss sum type.
For a CM-extension, we studied both theoretically and numerically a problem that the Stickelberger element is in the Fitting ideal of the dual of the ideal class group.
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