2017 Fiscal Year Final Research Report
Systematic constructions of supersingular Drinfeld modules
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 |
Research Field |
Algebra
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Research Institution | Shiga University |
Principal Investigator |
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Project Period (FY) |
2015-04-01 – 2018-03-31
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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 |
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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Free Research Field |
代数学
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