1998 Fiscal Year Final Research Report Summary
Theory of mixed motives and theory of scissors congruence groups of algebraic polyhedra
| Project/Area Number |
09440019
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
HANAMURA Masaki Kyushu Univ., Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (60189587)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Masaaki Kyushu Univ., Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (30030787)
KANEKO Masanobu Kyushu Univ., Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (70202017)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Chow groups / triangulated category / decomposition theorem / t-structure / twisted cohomology / Riemann's inequality |
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| Research Abstract |
In paper 1 the triangulated category of mixed motives over a field D(k) was constructed. This theory has been conjectured to exist since the early 1980's. The theory is expected have much application. In paper 2, the existence of an appropriate t-structure on D(k) has been studied assuming some "standard conjectures". I showed how to associate to a projective variety its motive, an object of D(k), in paper 3. We explored the motivic analogue of the "decomposition theorem" for the direct image of the constant sheaf under a proper map, paper 4. This includes the framework of motivic sheaves over an arbitrary variety.
In paper 5, Hanamura and M.Yoshida studied Hodge theory on twisted cohomology, and applied it to derive the analogue of Riemann's inequality.
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