2010 Fiscal Year Final Research Report
Research on explicit constructions of motives associated to automorphic forms
| Project/Area Number |
19740017
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Osaka Prefecture University (2008-2010)
Hiroshima University (2007) |
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Principal Investigator |
YAMAUCHI Takuya Osaka Prefecture University, 総合教育研究機構, 教育拠点形成教員 (90432707)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 保型形式 / ガロア表現 / L関数 |
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| Research Abstract |
(1) A construction of Siegel paramodular form corresponding to some rigid Calabi-Yau threefold.
(2) A construction of endoscopic lifts associated to some Siegel modular variety and a computation of L-function of that variety.
(3) A construction of a Calabi-Yau family having continuous Hodge number over the projective line minus three points and potential automorphy of each fiber.
For (3), we explain more concretely. From local systems of rank one over the open curve U : projective line minus three points, by using convolution we construct hypergeometric sheaves F_n/U of rank n+1, weight n for each natural number n and then we construct a Calabi-Yau family whose middle cohomology sheave realizes F_n up to algebraic cycles when n is even. As an application, we prove potential automorphy of each fiber.
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