2023 Fiscal Year Final Research Report
Slopes of Drinfeld modular forms
| Project/Area Number |
20K03545
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Tokyo City University |
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Principal Investigator |
Hattori Shin 東京都市大学, 理工学部, 准教授 (10451436)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | Drinfeld保型形式 / 傾斜 / D楕円層 |
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| Outline of Final Research Achievements |
In this research project I studied arithmetic of slopes of Drinfeld modular forms. Among others, I proved the triviality of the Hecke action on the space of Drinfeld cusp forms of level Γ1(t^n). This is a negative answer to a question of Gekeler stated in 1980s.
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| Free Research Field |
数論
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| Academic Significance and Societal Importance of the Research Achievements |
本研究で得られた傾斜0部分へのHecke作用の自明性は楕円保型形式では知られていない，Drinfeld保型形式特有の現象である．また，楕円保型形式で成立している弱重複度1と呼ばれる性質が重さを固定してもDrinfeld保型形式では成立しない，ということもここから従う．本研究成果はこのように，楕円保型形式にないDrinfeld保型形式の特異性を明らかにしたという点で意義深いものである．
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