Milnor type K-group attached to algebraic groups and arithmetic geometry
Project/Area Number |
25800019
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Hiroshima University |
Principal Investigator |
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 類体論 / 類数 / 数論的基本群 / 局所体 / 楕円曲線 / Chow 群 |
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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Report
(5 results)
Research Products
(10 results)