Applications of class field theory for curves over local fields
| Project/Area Number |
17K05174
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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 | Kyushu Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 類体論 / 楕円曲線 / 類数 / 類群 / 数論幾何学 |
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| Outline of Final Research Achievements |
The results in this project are mainly the following four: 1. First, I completed the class theory on open curves over local fields (which may has positive characteristic). 2. The lower bound of the class number associated with an elliptic curve over a number field is given by the rank of the Mordell-Weil group of the elliptic curve. 3. For a curve over a p-adic field, when the associated Jacobian variety has a good ordinary reduction, we obtain an explicit computation of the "class group" of the curve. 4. We discussed conditions under which the Somekawa K-group associated with two elliptic curves on a p-adic field becomes p-divisible.
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| Academic Significance and Societal Importance of the Research Achievements |
局所体上の曲線に対する類体論そのものは1980年代に完成していたが、付随する「類群」の計算についての結果はこれまでそれほど多くはなかった。今回の研究成果により、こうした「類群」を幾つかの場合は具体的に計算することが分かった。将来的な発展の余地も大きいと思われる。
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Report
(4 results)
Research Products
(11 results)
