Construction of the realization functors of motives

• Project/Area Number: 25400004
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: University 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: ¥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)
• Keywords: Hodge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.

Research Products

• [Journal Article] The Hodge ralization of mixed Tate motives (2013)
  • Author(s): Kenichiro Kimura
  • Journal Title: 数理解析研究所講究録 Volume: 1840 Pages: 139-148
  • Peer Reviewed
• [Presentation] Hodge realization of Bloch-Kriz mixed Tate motives via integral of logarithmic forms (2017)
  • 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)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Semi-algebraic chains and the Hodge realization of mixed Tate motives (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Hodge realization of mixed Tate motives (2014)
  • 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
  • Invited