| 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)
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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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