study of arithmetic properties of motives

• Project/Area Number: 19540007
• 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 University of Tsukuba, 大学院・数理物質科学研究科, 講師 (50292496)
• Co-Investigator(Kenkyū-buntansha): KIMURA Shun-ichi 広島大学, 大学院・理学研究科, 准教授 (10284150) ; BANNAI Kenichi 慶應義塾大学, 理工学部, 講師 (90343201)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: モチーフ / 代数学 / 代数的サイクル / 楕円ポリログ

Research Abstract

We studied higher 1-adic Abel-Jacobi map which is a method to detect algebraic cycles over number fields. Using Nori's construction of the category of motives, we obtained a simple description of higher Abel-Jacobi map. We give an alternate proof of a Theorem of Jannsen on the second Abel-Jacobi map. We have started the construction of the category of mixed elliptic motives.

Research Products

• [Journal Article] A remark on the second Abel-Jacobi map} (2008)
  • Author(s): K. Kimura
  • Journal Title: to appear in the proceedings of Tata international colloquium on cycles, motives and Shimura varieties
  • Peer Reviewed
• [Journal Article] Nori's construction and the second Abel-Jacobi map} (2007)
  • Author(s): K. Kimura
  • Journal Title: Mathematical Research Letters(K. Kimura) 14, no.6 Pages: 973-981
  • NAID: 120007138893
  • Peer Reviewed
• [Journal Article] Murre's conjectures for certain product varieties} (2007)
  • Author(s): K. Kimura
  • Journal Title: J.Math.Kyoto Univ.(K. Kimura) 47-3 Pages: 621-629
  • Peer Reviewed
• [Journal Article] Zero-cycles on self-product of modular curves} (2007)
  • Author(s): K. Kimura
  • Journal Title: Math.Z.(K. Kimura) 256 Pages: 563-571
  • Peer Reviewed
• [Journal Article] Zero-cycles on self-product of modular curves (2007)
  • Author(s): Kenichiro Kimura
  • Journal Title: Mathematische zeitschrift 256 Pages: 563-571
  • Peer Reviewed
• [Journal Article] Murre's conjectures for certain product varieties (2007)
  • Author(s): Kenichiro Kimura
  • Journal Title: Journal of Mathematics of Kyoto University 47 Pages: 621-629
  • Peer Reviewed
• [Journal Article] Nori's construction and the second Abel-Jacobi map (2007)
  • Author(s): Kenichiro Kimura
  • Journal Title: Mathematical Research Letters 14 Pages: 973-981
  • NAID: 120007138893
  • Peer Reviewed
• [Presentation] Mixed elliptic motives (2010)
  • Author(s): K. Kimura
  • Organizer: Weekend workshop on algebraic varieties
  • Place of Presentation: Fields Institute, Toronto
  • Year and Date: 2010-03-07
• [Presentation] Mixed elliptic motives (2010)
  • Author(s): 木村健一郎
  • Organizer: Weekend workshop on algebraic varieties
  • Place of Presentation: Fields Institute, Toronto, Canada
  • Year and Date: 2010-03-06
• [Presentation] 混合楕円モチーフ (2010)
  • Author(s): 木村健一郎
  • Organizer: 周期積分とモチーフ
  • Place of Presentation: 東京大学数理科学研究科
  • Year and Date: 2010-02-18
• [Presentation] Irrationality of Chow-Motivic zeta (2008)
  • Author(s): 木村俊一
  • Organizer: 筑波大学セミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2008-12-10
• [Presentation] On mixed elliptic motives (2008)
  • Author(s): 木村健一郎
  • Organizer: Number theory and Physics at crossroads
  • Place of Presentation: 津田塾大学
  • Year and Date: 2008-08-04
• [Presentation] Motivic zeta function in additive monoidal categories (2008)
  • Author(s): 木村俊一
  • Organizer: 広島大学代数学セミナー
  • Place of Presentation: 広島大学
  • Year and Date: 2008-05-16
• [Presentation] On the second Abel-Jacobi map (2008)
  • Author(s): Kenichiro Kimura
  • Organizer: Autour des cycles algebr iques
  • Place of Presentation: Institute de mathematiques de Jussieu
  • Year and Date: 2008-03-19
• [Presentation] On the second Abel-Jacobi map (2008)
  • Author(s): K. Kimura
  • Organizer: International colloquium on "Cycles, Motives and Shimura varieties"
  • Place of Presentation: Tata Institute, Mumbai
  • Year and Date: 2008-01-10
• [Presentation] On the second Abel-Jacobi map (2008)
  • Author(s): Kenichiro Kimura
  • Organizer: Cycles, motives and Shimura varieties
  • Place of Presentation: Tata Institute
  • Year and Date: 2008-01-10