| Project/Area Number |
17K05177
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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 | Tokyo City University (2018-2019)
Kyushu University (2017) |
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Principal Investigator |
HATTORI Shin 東京都市大学, 知識工学部, 准教授 (10451436)
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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 |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | Drinfeld保型形式 / 関数体 / 合同 / 傾斜 / 過収束Drinfeld保型形式 / 標準部分群 / Hodge-Tate-田口写像 / 過収束保型形式 |
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| Outline of Final Research Achievements |
I studied P-adic properties of Drinfeld modular forms over the rational function field over a finite field, and obtained the following. (1) I proved the p-adic local constancy of the dimension of generalized eigenspaces for the U_t operator acting on the space of Drinfeld modular forms, with respect to weights. This is a Drineld analogue of the Gouvea-Mazur conjecture in the elliptic case and published online. (2) I constructed P-adic continuous families of Drinfeld modular forms and, as an application, proved the triviality of the Hecke action on the space of ordinary Drinfeld cuspforms of certain level. (3) I obtained a generalization of the triviality of (2) to the case of level t square.
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| Academic Significance and Societal Importance of the Research Achievements |
Drinfeld保型形式は楕円保型形式の関数体類似だが，楕円保型形式のp進的性質に対して，その類似であるDrinfeld保型形式のP進的性質の理解はほとんど進んでいない．本研究で得られた研究成果は，Drinfeld保型形式のP進的性質の解明を大きく推し進めるものである．また，通常Drinfeld保型形式へのHecke作用の自明性は，楕円保型形式の場合には見られなかった現象であり，Drinfeld保型形式のP進理論に関して新たな展開を予感させるという意味で意義深いものである．
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