• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Theory of mixed motives and theory of scissors congruence groups of algebraic polyhedra

Research Project

Project/Area Number 09440019
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKYUSHU 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)

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)
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)
KeywordsChow groups / triangulated category / decomposition theorem / t-structure / 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 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.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] M.Hanamura: "Mixed motives and algebraic cycles,II" submitted.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Hanamura: "Mixed motives and algebraic cycles,III" Mathematical Research Letters. to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Hanamura: "The mixed motive of a projective variety" CRM Proceedings of Banff conference on algebraic cycles. to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Corti and M.Hanamura: "Motivic decomposition and intersection Chow groups,I" Duke Math.J.to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Hanamura and M.Yoshida: "Hodge structures on twisted cohomology and twisted Riemann's inequality" Nagoya Math.J.to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Hanamura: "Mixed motives and algebraic cycles, II" (submitted).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Hanamura: "Mixed motives and algebraic cycles, III" Mathemtical Research Letters. (to ap-pear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Hanamura: "The mixed motive of a projective variety" CRM Proceedings of Banff conference on algebraic cyclesto appear. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Corti and M.Hanamura: "Motivic decomposition and inter-section Chow groups, I" Duke Math.J.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Hanamura and M.Yoshida: "Hodge structures on twisted cohomology and twisted Riemann's inequality" Nagoya Math.J.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Hanamura: "Mixed motives and algebraic cycles,II" (submitted).

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Hanamura: "Mixed motives and algebraic cycles,III" Mathematical Research Letters. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Hanamura: "The mixed motive of a projective variety" CRM Proceedings of Banff conference on algebraic cycles. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Corti and M.Hanamura: "Motivic decomposition and intersection Chow groups,I" Duke Math.J.(to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Hanamura and M.Yoshida: "Hodge structures on twisted cohomology and twisted Riemann‘s inequality" Nagoya Math.J. (to appear).

    • Related Report
      1998 Annual Research Report

URL: 

Published: 1998-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi