Theory of mixed motives and theory of scissors congruence groups of algebraic polyhedra
Project/Area Number  09440019 
Research Category 
GrantinAid for Scientific Research (B)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  KYUSHU UNIVERSITY 
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)

CoInvestigator(Kenkyūbuntansha) 
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)

Project Period (FY) 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,900,000 (Direct Cost : ¥1,900,000)
Fiscal Year 1998 : ¥1,900,000 (Direct Cost : ¥1,900,000)

Keywords  Chow groups / triangulated category / decomposition theorem / tstructure / twisted cohomology / Riemann's inequality / 混合モティーフ理論 / 代数多面体のscissors合同群の理論 / モチーフ理論 / モジュラー多様体 / 代数的サイクル 
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 tstructure 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.

Report
(3results)
Research Output
(15results)