1998 Fiscal Year Final Research Report Summary
P-adic L-functions of modular forms and the Euler systems
| Project/Area Number |
09640051
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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 | TOKYO METROPOLITAN UNIVERSITY |
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Principal Investigator |
KURIHARA Masato Tokyo Metropolitan University Associate Professor, 理学研究科, 助教授 (40211221)
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| Co-Investigator(Kenkyū-buntansha) |
KURANO Kazuhiko Tokyo Metropolitan University Associate Professor, 理学研究科, 助教授 (90205188)
NAKAMURA Ken Tokyo Metropolitan University Professor, 理学研究科, 教授 (80110849)
MIYAKE Katsuya Tokyo Metropolitan University Professor, 理学研究科, 教授 (20023632)
KATO Kazuya Tokyo University Professor, 数理科学研究科, 教授 (90111450)
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| Project Period (FY) |
1997 – 1998
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| Keywords | ideal class group / Iwasawa theory / Greenberg conjecture / maximal abelian extension |
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| Research Abstract |
We obtained several results, using the argument in the theory of Euler systems. First of all, we showed that the ideal class group of the maximal real subfield of the field which is obtained by adjoining all the roots of unify to a totally real number field, is trivial. Especially, every ideal of a real abelian field becomes principal in some real abelian field. In other words, the ideal class group of the field which is obtained by adjoing cos(ィイD72π(/)nィエD7) for all n > 0 over the rational number field is trivial. We also applied this method and obtained the triviality of the ideal class group of the maximal abelian extension of a number field which contains an imaginary quadratic field.
Next, using Deligne-Soule's cyclotomic elements, we made a simple criterion for Greenberg's conjecture on the ideal class groups of the cyclotomic ZィイD2pィエD2-extension of real abelian fields, and we carried out various numerical computation and checked the validity of this conjecture for small primes.
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