2015 Fiscal Year Final Research Report
Development of arithmetic topology and arithmetic quantum field theory
| Project/Area Number |
24340005
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Research Collaborator |
Terashima yuji
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 結び目 / 素数 / 3次元多様体 / 代数体 |
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| Outline of Final Research Achievements |
Based on the analogies between knots and primes, I studied arithmetic topology.
・We introduced the notion for S, which is a finite set S of primes of a number field containing a primitive m-th root of unity, to be link type. Then we introduce the multiple power residue symbols for such an S which generalize the power residue symbols and the Redei triple symbols. In particuler, we constructed the triple symbols over the cubic cyclotomic field. I wrote the joint paper with Fumiya Amano on this work (submitted). ・Following the analogies with Selmer module and the associated algebraic p-adic L-function for deformations of a Galois representation, we introduced the Selmer module and the associated L-function for deformations of a SL(2)-representation of a knot group, and gave an affirmative answer to Mazur's problem for some concrete examples. I wrote
the joint paper with Takahiro Kitayama, Ryoto Tange, Yuji Terashima on this work (submitted).
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| Free Research Field |
数論的位相幾何学
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