2014 Fiscal Year Final Research Report
Positively ramified extensions and elliptic units
| Project/Area Number |
24540028
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 整数論 / 岩澤理論 / ポジティブ分岐拡大 / 楕円単数 / 岩澤主予想 |
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| Outline of Final Research Achievements |
I studied Iwasawa theory for positively ramified extensions. The aims were: (a) to clarify properties of the "p-adic L-function" corresponding to the Galois group X of the maximal abelian pro-p extension which is p-ramified and positively ramified at p over a field of Z_p-extension, (b) to prove properties of X without "mu=0" assumption, and (c) to find more fine structures of X.
For (a), I obtained a result on certain functional equation of the "p-adic L function" when the base field is an abelian extension of an imaginary quadratic field, which I am preparing for publication. For (b), I had "a part of" functional equation of X for more general base field. For (c), I could not have enough progress and will continue my investigation.
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| Free Research Field |
代数学
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