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Construction of the realization functors of motives

Research Project

Project/Area Number 25400004
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionUniversity of Tsukuba

Principal Investigator

KIMURA Kenichiro  筑波大学, 数理物質系, 講師 (50292496)

Research Collaborator Terasoma Tomohide  
Hanamura Masaki  
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
KeywordsHodge実現 / Hodge realization / mixed Tate motives / semi-algebraic sets
Outline of Final Research Achievements

We succeeded in the construction of the Hodge realization functor on the category of mixed Tate motives in terms of period integrals. In the next paper we will prove that the functor we have constructed is equivalent to the original one defined by Bloch and Kriz. We will also construct the Hodge realization of mixed elliptic motives, and apply our results to the study of the period conjecture formulated by Kontsevich-Zagier.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (5 results)

All 2017 2015 2014 2013

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (4 results) (of which Int'l Joint Research: 2 results,  Invited: 4 results)

  • [Journal Article] The Hodge ralization of mixed Tate motives2013

    • Author(s)
      Kenichiro Kimura
    • Journal Title

      数理解析研究所講究録

      Volume: 1840 Pages: 139-148

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Hodge realization of Bloch-Kriz mixed Tate motives via integral of logarithmic forms2017

    • Author(s)
      Kenichiro Kimura
    • Organizer
      第12回 鹿児島 代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学理学部 (鹿児島県鹿児島市)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Semi-algebraic chains and the Hodge realization of mixed Tate motives.2015

    • Author(s)
      Kenichiro Kimura
    • Organizer
      Algebraic geometry
    • Place of Presentation
      Indian statistical institute Bangalore(India)
    • Year and Date
      2015-12-11
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Semi-algebraic chains and the Hodge realization of mixed Tate motives2015

    • Author(s)
      Kenichiro Kimura
    • Organizer
      TSUDA COLLEGE MINI-WORKSHOP ON CALABI-YAU VARIETIES:ARITHMETIC, GEOMETRY AND PHYSICS
    • Place of Presentation
      津田塾大学(東京都小平市)
    • Year and Date
      2015-08-05
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Hodge realization of mixed Tate motives2014

    • Author(s)
      木村健一郎
    • Organizer
      玉原特殊多様体研究集会
    • Place of Presentation
      玉原セミナーハウス(沼田市)
    • Year and Date
      2014-09-18
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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