Theory of mixed motivic sheaves and mixed Tate motives
| Project/Area Number |
24540033
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tohoku University |
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Principal Investigator |
Hanamura Masaki 東北大学, 理学(系)研究科(研究院), 教授 (60189587)
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| Co-Investigator(Renkei-kenkyūsha) |
TERASOMA TOMOHIDE 東京大学, 数理科学研究科, 教授 (50192654)
KIMURA KENICHIRO 筑波大学, 数理物質科学研究科, 講師 (50292496)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | algebraic cycles / motives / triangulated category / cohomology / semi-algebraic set / logarithmic form / Cauchy formula / 混合モティーフ / Hodge structure / モティーフ / Chow群 / 代数的サイクル / コホモロジー / 三角圏 |
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| Outline of Final Research Achievements |
We studied the theory of integrals of differential forms with logarithmic singularities on semi-algebraic sets; we gave a sufficient geometric condition for the convergence of the integral. Also, we formulated and proved a higher dimensional generalization of the Cauchy formula in complex analysis. We developed the basic theory of quasi DG category, a notion had been previously proposed by the investigator; in particular, we gave a method to produce a triangulated category out of a quasi DG category. Using this, we constructed the triangulated category of mixed motivic sheaves over an arbitrary algebraic variety. We studied the relationship between the triangulated category of mixed Tate motives, and the abelian category of co-modules over the bar complex of the cycle complex.
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Report
(5 results)
Research Products
(12 results)
