A research on a new symmetry on motive with real multiplication
| Project/Area Number |
16K13742
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
山本 修司 慶應義塾大学, 理工学研究科(矢上), 准教授 (20635370)
坂内 健一 慶應義塾大学, 理工学部(矢上), 准教授 (90343201)
安田 正大 大阪大学, 理学研究科, 准教授 (90346065)
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| Research Collaborator |
OTA Kazuto 慶応大学, 理工学部, 特任助教 (70770775)
HAGIHAEA Kei 慶応大学, 理工学部, 助教 (30512173)
YAMADA Kazuki 慶応大学, 理工学研究科, 特別研究員(DC2)
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| Project Period (FY) |
2016-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 整数論 / L-関数 / モチーフ / 総実体 / ポリロガリズム / Hodge構造 / L-関数の特殊値 / 代数 / 実乗法 / 数論幾何 / 数論幾何学 / 代数的整数論 / Bloch-Kato予想 |
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| Outline of Final Research Achievements |
Plectic conjecture by J. Nekovar and A. Scholl is considered to give a strong impact on the study for motive with real multiplication if the program is completed. However, the program has just started. We studied the Hodge realization of the plectic cohomology. We gave an equivalent description of mixed plectic Hodge structures in terms of the weight and partial Hodge filtrations. We also constructed an explicit complex calculating the extension groups in this category. This result is important to consider applications to concrete problems.
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Report
(3 results)
Research Products
(8 results)
