2016 Fiscal Year Final Research Report
Milnor type K-group attached to algebraic groups and arithmetic geometry
| Project/Area Number |
25800019
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 類体論 / 類数 / 数論的基本群 |
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| Outline of Final Research Achievements |
The results obtained during the research period are as follows: 1. For some elliptic curves over a p-adic field, we show a conjecture due to Somekawa on the Galois symbol map. Results have been published in Funct. Approx. Comment. Math. 2. We investigate the class field theory for an open curve over a local field. 3. We show the finiteness of etale coverings of such a variety with given degree whose ramification bounded along an effective Cartier divisor. This can be thought of a higher dimensional analogue of the classical Hermite-Minkowski theorem. 4. We give a lower bound of the class number of the number field associated to the p-power division points of elliptic curves over Q
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| Free Research Field |
数論幾何学
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