Study of mixed motives by the bar construction

Research Project

Project/Area Number	17K05157
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)
Project Period (FY)	2017-04-01 – 2023-03-31
Project Status	Completed (Fiscal Year 2022)
Budget Amount *help	¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000) Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000) Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000) Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords	周期積分 / perid integral / admissible chains / Abel-Jacobi map / higher Chow cycle / 高次Chowサイクル / Abel-Jacobi写像 / Hodge realization / 代数学
Outline of Final Research Achievements	The motivation of this research was to understand the Hodge realization of mixed Tate motives. We constructed ceratain complex of topological chains which we call admissible chains. Via this complex we constructed a Hodge realization functor of mixed Tate motives, and a description of the Abel-Jacobi map of higher Chow cycles.
Academic Significance and Societal Importance of the Research Achievements	これまで構成されたモチーフの圏の実現関手は、ある意味で明快だが高度に抽象的であった。具体的な構成を与えたことで、より周期積分との関係が明らかになった。