2012 Fiscal Year Final Research Report
Study of non-abelian number theory based on Iwasawa theory
| Project/Area Number |
21540030
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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 | Waseda University (2011-2012)
Kinki University (2009-2010) |
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Principal Investigator |
OZAKI Manabu 早稲田大学, 理工学術院, 教授 (80287961)
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| Research Collaborator |
MIZUSAWA Yasushi 名古屋工業大学, 准教授 (60453817)
ITOH Tsuyoshi 千葉工業大学, 講師
TOHKAILIN Mitsul 大阪工業大学, 非常勤講師
FUJII Satoshi 金沢工業大学, 講師 (20386618)
OKANO Keiji 都留文科大学, 講師
MAIRE Christian Universite de Franche-Comte, 教授
ABBAS Chazad Movahhedi Universite de Limoges, 教授
BRUNO Angles Universite de Caen, 教授
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| Project Period (FY) |
2009 – 2012
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| Keywords | 数論 / 代数体 / 岩澤理論 / ガロワ群 / 非アーベル拡大 |
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| Research Abstract |
In this research project, I have obtained results on (1) a formula describing Z_p-rank of tamely ramified Iwasawa modules of the basic Z_p-extension, (2) an analogy of Weil paring for ideal class groups of number fields, (3) the isomorphism classes of Galois cohomology groups of global unit groups, and (4) a characterization of the Dedekind zeta functions in terms of a family of the Galois groups of restricted ramified extensions.
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