| Project/Area Number |
15K17508
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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 | Shiga University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
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| Keywords | 超特異ドリンフェルト加群 / ドリンフェルト加群 / 超特異多項式 / 超特異点 / 有限体上の関数体の塔 / 関数体の塔 / 有限体 / 有理点 / ドリンフェルト・モジュラー多様体 / ドイリング多項式 / 超幾何関数 / ドリンフェルト・モジュラー曲線 / 志村曲線 / 数論的三角群 / 基本対称式 / 関数等式 |
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| Outline of Final Research Achievements |
(1) I gave explicitly the coefficients of supersingular Drinleld modules of arbitrary rank. By using this result, I proved a necessary and sufficient condition for supersingularity. Moreover, I computed several rank-2 (resp. rank-3) supersingular Drinfeld modules, which are not isomorphic each other.
(2) I gave explicitly the coefficients of rank-2 supersingular Drinleld modules, which is more explicitly than (1). As its application, I constructed an asymptotically optimal towers over finite fields.
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