Geometry and arithmetic of period integrals and motives
| Project/Area Number |
23340001
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TERASOMA Tomohide 東京大学, 数理(科)学研究科(研究院), 教授 (50192654)
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| Co-Investigator(Kenkyū-buntansha) |
HANAMURA Masaki (SHIHO Atsushi / MATSUMOTO Keiji / KIMURA Kenichirou) 東北大学, 理学研究科, 教授 (60189587)
松本 圭司 北海道大学, 理学(系)研究科(研究院), 教授 (30229546)
志甫 淳 東京大学, 数理(科)学研究科(研究院), 教授 (30292204)
木村 健一郎 筑波大学, 数理物質科学研究科(系), 講師 (50292496)
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| Project Period (FY) |
2011-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥12,740,000 (Direct Cost: ¥9,800,000、Indirect Cost: ¥2,940,000)
Fiscal Year 2014: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
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| Keywords | モチーフ / 周期積分 / 代数的サイクル / コホモロジー / 周期写像 / ホッジ理論 / 算術幾何 / テータ関数 / モジュラー多様体 |
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| Outline of Final Research Achievements |
We construct a complex using semi-algebraic set and prove generalized Cauchy formula to construct a Hodge realization functor of mixed Tate motives.
We introduce a motivic filtration which gives a depth filtration. We construct surfaces which have big images of cycle maps from higher Chow groups to cohomologies.
We study Schwarz maps for reducible hypergeometric systems of two variable with a special parameter. We describe the inverse period map using theta function. We give a description of the image of Abel-Jacobi map corresponding to a family of genus two curves.
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Report
(5 results)
Research Products
(42 results)
