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 |
Research Field |
Algebra
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Research Institution | Osaka Prefecture University (2008-2010) Hiroshima University (2007) |
Principal Investigator |
YAMAUCHI Takuya Osaka Prefecture University, 総合教育研究機構, 教育拠点形成教員 (90432707)
|
Project Period (FY) |
2007 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥3,920,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
|
Keywords | 保型形式 / ガロア表現 / L関数 / 潜在的保型 / Calabi-Yau族 / エンドスコピー / 岩沢理論 / ガロアコホモロジー / モジュラー多様体 / 保型性 / 変形理論 / p進Hodge理論 / モジュラー性 / R=T / GSp(4) |
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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Report
(6 results)
Research Products
(52 results)
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[Presentation] ガロア表現概説I2009
Author(s)
山内卓也
Organizer
2009整数論サマースクールにおける, 口頭発表
Place of Presentation
京都アピカルイン
Year and Date
2009-08-19
Related Report
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[Presentation] ガロア表現概説I2009
Author(s)
山内卓也
Organizer
整数論サマースクール
Place of Presentation
京都アピカルイン(京都府)
Year and Date
2009-08-19
Related Report
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