Mixed motivic sheaves, category theory, and study of cycle complexes
| Project/Area Number | 21340002 |
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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 | Tohoku University |
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Principal Investigator |
HANAMURA Masaki 東北大学, 大学院・理学研究科, 教授 (60189587)
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| Co-Investigator(Renkei-kenkyūsha) |
KIMURA Shunichi 広島大学, 大学院・理学研究科, 教授 (10284150)
ISHIDA Masanori 東北大学, 大学院・理学研究科, 教授 (30124548)
YUKIE Akihiko 京都大学, 大学院・理学研究科, 教授 (20312548)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed(Fiscal Year 2011)
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| Budget Amount *help |
¥6,630,000 (Direct Cost : ¥5,100,000、Indirect Cost : ¥1,530,000)
Fiscal Year 2011 : ¥2,210,000 (Direct Cost : ¥1,700,000、Indirect Cost : ¥510,000)
Fiscal Year 2010 : ¥2,210,000 (Direct Cost : ¥1,700,000、Indirect Cost : ¥510,000)
Fiscal Year 2009 : ¥2,210,000 (Direct Cost : ¥1,700,000、Indirect Cost : ¥510,000)
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| Keywords | 代数幾何学 / モティーフ理論 / 三角圏 / 代数的サイクル / モティーフ / Chow群 / 代数サイクル / コホモロジー / チャウ群 |
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| Research Abstract |
Quasi DG category, a generalization of DG category given by the principal researcher, is a notion that appears in the theory of mixed motivic sheaves. We developed the basic theory of quasi DG categories. The mail features are basic axioms of a quasi DG category, the notion of C-diagrams with values in a quasi DG category, additivity of the function complexes, the construction of the quasi DG category of C-diagrams, and the proof that the homotopy category of the quasi DG category of C-diagrams has the structure of a triangulated category.In particular, when the function complex (depending on n objects) that constitutes part of the notion, is additive in each variable, the same property was proven to hold for the function complex for C-diagrams.
We described the Chow cohomology of an algebraic surface using its resolution of singularities. In particular, we gave a condition for Chow cohomology and homology to coincide.
We showed the blow-up formula for the motives and higher Chow groups of a quasi-projective variety.
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Report
(4results)
Research Products
(20results)
