Theory of mixed motivic sheaves and mixed Tate motives

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540033
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: Hanamura Masaki 東北大学, 理学(系)研究科(研究院), 教授 (60189587)
• Co-Investigator(Renkei-kenkyūsha): TERASOMA TOMOHIDE 東京大学, 数理科学研究科, 教授 (50192654) ; KIMURA KENICHIRO 筑波大学, 数理物質科学研究科, 講師 (50292496)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: algebraic cycles / motives / triangulated category

Outline of Final Research Achievements

We studied the theory of integrals of differential forms with logarithmic singularities on semi-algebraic sets; we gave a sufficient geometric condition for the convergence of the integral. Also, we formulated and proved a higher dimensional generalization of the Cauchy formula in complex analysis. We developed the basic theory of quasi DG category, a notion had been previously proposed by the investigator; in particular, we gave a method to produce a triangulated category out of a quasi DG category. Using this, we constructed the triangulated category of mixed motivic sheaves over an arbitrary algebraic variety. We studied the relationship between the triangulated category of mixed Tate motives, and the abelian category of co-modules over the bar complex of the cycle complex.

Free Research Field

Algebraic Geometry