1998 Fiscal Year Final Research Report Summary
Arithmetic of Z_p-field and geometry of algebraic curves
| Project/Area Number |
09640008
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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 (1998)
The University of Tokyo (1997) |
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Principal Investigator |
NAKAJIMA Shoichi Gakushuin University, Faculty of Science, Professor, 理学部, 教授 (90172311)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMOTO Fuminori Gakushuin University, Faculty of Science, Assistant, 理学部, 助手 (50195161)
NAKANO Shin Gakushuin University, Faculty of Science, Associate Professor, 理学部, 助教授 (40180327)
ICHIMURA Humio Yokohama City University, Faculty of Science, Associate Professor, 理学部, 助教授 (00203109)
NAITO Hirotada Kagawa University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00180224)
KURODA Shigenobu University of Tokyo, Graduate School of Mathematical Sciences, Associate Profess, 大学院・数理科学研究科, 助教授 (70012416)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Iwasawa theory / Algebraic number field |
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| Research Abstract |
The aim of this project was investigating Iwasawa theory of algebraic number fields through the notion of Zp-field, and through comparing it with the arithmetic theory of elliptic curves.
The results obtained in the project are concerned with
(1) basic construction of Iwasawa theory
(2) arithmetic of elliptic curves over algebraic number fields, and they are collected in the publication of the results of this project.
In this project the following activities were also proceeded :
(3) activity of "Kummer Research Group"
(4) computation of examples by using computer algebra system.
(3) is a project for reading papers of Kummer on number theory, expecting to find new ideas in classical great works.
(4) is an attempt to find good examples for Iwasawa theory by making use of computers whose ability is extensively advanced recently.
For (3) and (4) no concrete results have been published yet.
However, in future we expect to publish, in some form, the results of activities (3) and (4) that were begun as part of this project.
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