Study of the mixed elliptic motives

• Project/Area Number: 22540008
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• 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)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 数論幾何学 / ホッジ実現 / モチーフ

Research Abstract

Generalizing the Bloch-Kriz construction of mixed Tate motives, We constructed a Hopf algebra which should be the Galois group of the category of the Mixed elliptic motives. The method is by the bar construction of a differentialgraded algebra constructed from algebraic cycles on the products of an ellipticcurve and affine spaces. The motive of the elliptic polylogarithm exists in ourcategory.

Research Products

• [Journal Article] Motivic zeta functions in additive monoidal categories (2012)
  • Author(s): K. Kimura, S. Kimura, N. Takahashi
  • Journal Title: Journal of K-theory Volume: 9 Pages: 459-473
  • URL: http://dx.doi.org/10.1017/is011011006jkt174
  • Peer Reviewed
• [Journal Article] Motivic zeta functions in additive monoidal categories (2012)
  • Author(s): K.Kimura, S.Kimura, N.Takahashi
  • Journal Title: Journal of K-theory Volume: (To appear) Pages: 1-15
  • Peer Reviewed
• [Journal Article] A Remark on the SecondAbel-Jacobi map (2010)
  • Author(s): K. Kimura
  • Journal Title: Cycles, Motives and Shimura varieties Pages: 217-226
  • Peer Reviewed
• [Journal Article] A Remark on the Second Abel-Jacobi map (2010)
  • Author(s): K.Kimura
  • Journal Title: Cycles, Motives and Shimura varieties Volume: 1 Pages: 217-226
  • Peer Reviewed
• [Presentation] Hodge realization of mixedTate motives (2012)
  • Author(s): 木村健一郎
  • Organizer: ホップ代数と量子群-応用 の可能性
  • Place of Presentation: 京都大学
  • Year and Date: 2012-09-04
• [Presentation] Hodge realization of mixed Tate motives via period integral (2012)
  • Author(s): 木村健一郎
  • Organizer: 代数幾何とモチーフ理論ワークショップ
  • Place of Presentation: 東北大学
  • Year and Date: 2012-03-08
• [Presentation] Hodge realization of mixed Tate motives via period integral (2012)
  • Author(s): 木村健一郎
  • Organizer: 代数幾何とモチーフ理論ワークショップ
  • Place of Presentation: 東北大学(仙台市)(招待講演)
  • Year and Date: 2012-03-08
• [Presentation] Hodge realization of mixed Tate motives (2012)
  • Author(s): 木村健一郎
  • Organizer: ホップ代数と量子群-応用の可能性
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] Hodge realization of mixedTate motives via period integral (2011)
  • Author(s): 木村健一郎
  • Organizer: 玉原特殊多様体研究集会
  • Place of Presentation: 東京大学玉原セミナーハウス
  • Year and Date: 2011-09-06
• [Presentation] Hodge realization of mixed Tate motives (2011)
  • Author(s): 木村健一郎
  • Organizer: 玉原特殊多様体研究集会
  • Place of Presentation: 東京大学玉原セミナーハウス(沼田市)(招待講演)
  • Year and Date: 2011-09-06
• [Presentation] Mixed Elliptic Motives (2010)
  • Author(s): K. Kimura
  • Organizer: NUMBER THEORY, GEOMETRY ANDPHYSICS AT THE CROSSROADS
  • Place of Presentation: 津田塾大学
  • Year and Date: 2010-08-08
• [Presentation] Mixed Elliptic Motives (2010)
  • Author(s): K.Kimura
  • Organizer: NUMBER THEORY, GEOMETRY AND PHYSICS AT THE CROSSROADS
  • Place of Presentation: 津田塾大学(小平市)(招待講演)
  • Year and Date: 2010-08-08