2005 Fiscal Year Final Research Report Summary
Applications of the theory of mixed motifs
| Project/Area Number |
15340013
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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 Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60189587)
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| Co-Investigator(Kenkyū-buntansha) |
KANEKO Masanobu Kyushu University, Graduate School of Mathematical Science, Professor, 大学院・数理学研究科, 教授 (70202017)
MORITA Yasuo Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20011653)
ISHIDA Masanori Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30124548)
YUKIE Akihiko Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20312548)
SAITO Shuji University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (50153804)
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| Project Period (FY) |
2003 – 2005
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| Keywords | motif / algebraic cycles / cohomology |
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| Research Abstract |
1. For a variety with singularities, a theorem of Barthel, Brasselet, Fiesler, Gabber and Kaup asserts that the cycle class of an algebraic cycle in Borel-Moore homoloty can be lifted to a class in intersection cohomology. We gave an alternative proof of this theorem based on the decomposition theorem. Further we formulated a motivic analogue of this theorem, and proved it holds true under the "standard" conjectures on algebraic cycles (due to Grothendieck, Bloch-Beilinson-Murre, and Beilinson-Soule).
2. We gave a definition of intersection Chow group, which is a motivic analogue of intersection cohomology. We gave a detailed account of this theory in a paper.
3. We showed the motivic motivic decomposition theorem (motivic analogue of the decomposition theorem) holds for a Lefschetz pencil with a surface as the total space. The same holds under some hypotheses for a Lefschetz pencil of any dimension.
4. We wrote a paper on the construction of the triagulted category of mixed motivic sheaves over a base variety. This generalizes our previously established theory over a field.
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Research Products
(6 results)
