2008 Fiscal Year Final Research Report
Iwasawa theory for anti-cyclotomic extensions and for positivelyramified extensions
| Project/Area Number |
20740025
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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 | Tokyo University of Science |
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Principal Investigator |
八森 祥隆 Tokyo University of Science, 理工学部, 講師 (50433743)
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| Project Period (FY) |
2008 – 2009
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| Keywords | 数論 / 岩澤理論 / 岩澤主予想 / セルマー群 |
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| Research Abstract |
I studied a relationship between both the Selmer groups and p-adic L-functions for two Galois representations which are congruent modulo p-power over anti-cyclotomic Z_p-extensions. I got a satisfactory result about the Selmer groups. For p-adic L-functions, I examined a new construction for those, which would be a key to proving the relationship. I also studied Iwasawa theory for positively-ramified extensions and got a kind of p-adic L-functions and proved the main conjecture for abelian extensions of imaginary quadratic fields.
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