Iwasawa theory for abelian extensions over imaginary quadratic fields and elliptic units
| Project/Area Number |
19740020
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Okayama University of Science |
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Principal Investigator |
AOKI Miho Okayama University of Science, 総合理工学部, 准教授 (10381451)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,140,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥540,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | イデアル類群 / ガウス和 / 円単数 / 楕円単数 / 代数的K群 / Brumer予想 / Coates-Sinnott予想 / 部分ゼータ関数 / Stickelberger元 / 数論 / 岩澤理論 |
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| Research Abstract |
I studied the relation between Brumer conjecture and Coates-Sinnott conjecture. The former is related to ideal class groups of number fields, and the latter is related to K-groups of the rings of integers. In my paper "A note on the Coates-Sinnott conjecture, Bulletin of the London Mathematical Society 41, 613-620, 2009", I proved that the former conjecture implies the latter conjecture under some assumptions. In another paper "On some exact sequences in the theory of cyclotomic fields, Journal of Algebra 320, 4156-4177, 2008", I showed the existence of some exact sequences which relate both the plus part and the minus part of Iwasawa modules. Furthermore, I formulated some conjecture about K-groups of the rings of integers of cyclotomic fields, and described an order of etale cohomology groups by using cyclotomic units and Gauss sums. At the end of the study, I considered general abelian number fields and abelian extensions over imaginary quadratic fields.
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Report
(6 results)
Research Products
(11 results)
