Geometry and arithmetic of period integrals and motives

2014 Fiscal Year Final Research Report

• Project/Area Number: 23340001
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: TERASOMA Tomohide 東京大学, 数理(科)学研究科(研究院), 教授 (50192654)
• Co-Investigator(Kenkyū-buntansha): HANAMURA Masaki 東北大学, 理学研究科, 教授 (60189587) ; KIMURA Kenichirou 筑波大学, 数理物質科学研究科, 講師 (60189587) ; MATSUMOTO Keiji 北海道大学, 理学研究科, 教授 (60189587) ; SHIHO Atsushi 東京大学, 数理科学研究科, 教授 (60189587)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: モチーフ / 周期積分 / 代数的サイクル / コホモロジー

Outline of Final Research Achievements

We construct a complex using semi-algebraic set and prove generalized Cauchy formula to construct a Hodge realization functor of mixed Tate motives.
We introduce a motivic filtration which gives a depth filtration. We construct surfaces which have big images of cycle maps from higher Chow groups to cohomologies.
We study Schwarz maps for reducible hypergeometric systems of two variable with a special parameter. We describe the inverse period map using theta function. We give a description of the image of Abel-Jacobi map corresponding to a family of genus two curves.

Free Research Field

代数幾何