Theory of congruences of Galois representations and modular forms for function fields
| Project/Area Number |
26400016
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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 University |
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Principal Investigator |
Hattori Shin 九州大学, 数理学研究院, 助教 (10451436)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | Drinfeld保型形式 / 固有値多様体 / eigenvariety / 標準部分群 / 保型形式 |
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| Outline of Final Research Achievements |
The aim of this research project was to construct a theory of v-adic congruences for Drinfeld modular forms. Using Taguchi's duality, I defined the Hodge-Tate-Taguchi map, which is a torsion comparison isomorphism for the Drinfeld setting. With this map, I proved that Drinfeld modular forms with highly congruent Fourier expansions have highly congruent weights, and also that any Drinfeld modular form of tame level n is a v-adic modular form.
I also studied the geometry of eigenvarieties, for future applications to Drinfeld modular forms. I proved the properness of Hilbert eigenvarieties at integral weights and a conjecture of Coleman-Mazur on irreducible components of Coleman-Mazur eigencurves of finite degree.
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Report
(4 results)
Research Products
(21 results)
