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2002 Fiscal Year Final Research Report Summary

Theory of motives and algebraic cycles

Research Project

Project/Area Number 12440009
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 University, Graduate School of Mathematics, Ass. Prof., 大学院・数理学研究院, 助教授 (60189587)

Co-Investigator(Kenkyū-buntansha) SATO Eiichi  Kyushu University, Graduate School of Mathematics, Prof., 大学院・数理学研究院, 教授 (10112278)
YOSHIDA Masaaki  Kyushu University, Graduate School of Mathematics, Prof., 大学院・数理学研究院, 教授 (30030787)
KANEKO Masanobu  Kyushu University, Graduate School of Mathematics, Prof., 大学院・数理学研究院, 教授 (70202017)
KIMURA Shun-ichi  Hiroshima University, Facility of Science, Lecturer, 理学部, 講師 (10284150)
SAITO Shuji  Nagoya University, School of Polymathematics, Prof., 大学院・多元数理科学研究科, 教授 (50153804)
Project Period (FY) 2000 – 2002
Keywordsmotif / decomposition theorem / modular varieties
Research Abstract

1. Motives of varieties: Let D(k) be the category of mixed motives over a field k. We produced a functor from the category of quasi-projective varieties into D(k). The construction uses the method of cubical hyperresolution.
2. Motivic decomposition theorem: It is of interest to formulate and prove the motivic analogue of the topological decomposition theorem (of Beilinson, Bernstein and Deligne). In the case of the universal family of abelian varieties over the Hilbert modular variety, we showed the existence of the expected motivic decomposition, and deduced from it the Grothendieck-Murre conjecture for the fiber variety.
3. Homology correspondence at chain level: It is well-known to consider homological correspondences and their compositions. We considered this at the chain level. Namely we gave a complex of abelian groups which gives cohomology, and produced the composition map as a map of complexes. This construction is applied to produce the cohomology realization functor from mixed motives.
4. Mixed motivic sheaves: We sketched the construction of the triangulated category of mixed motives over a quasi-projective variety.

  • Research Products

    (8 results)

All Other

All Publications (8 results)

  • [Publications] B.Gordon, M.Hanamura, J.P.Murre: "Relative Chow-Kunneth projectors for modular varieties"J. reine angew. Math.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] B.Gordon, M.Hanamura, J.P.Murre: "Chow-Kunneth projectors for modular varieties"Cornptes Rendues Math.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Corti, M.Hanamura: "Motivic decomposition and intersection Chow groups I"Duke Math. J.. 103. 459-522 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Hanamura: "Homological and cohomological motives of algebraic varieties"Invent. Math.. 142. 319-349 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] B. Gordon, M. Hanamura, and J.P. Murre: "Relative Chow-Kunneth projectors for modular varieties"J. reine angew. Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] B. Gordon, M. Hanamura, and J.P. Murre: "Chow-Kunneth projectors for modular varieties"Comptes Rendues Mathematique. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Corti and M. Hanamura: "Motivic decomposition and intersection Chow groups I"Duke Math. J.. 103. 459-522 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Hanamura: "Homological and cohomological motives of algebraic varieties"Invent. Math.. 142. 319-349 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2004-04-14  

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