Motive theory based on Weil reciprocity

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654001
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: YAMAZAKI Takao 東北大学, 理学(系)研究科(研究院), 教授 (00312794)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 数論幾何 / モチーフ

Outline of Final Research Achievements

Celebrated theory of mixed motives, due to Voevodsky, is yet to be extended in order to take into account non-homotopy invariant objects. Indeed, there are fundamental objects, such as relative Picard group of an algebraic curve, that are not homotopy invariant. By taking Weil reciprocity in the place of homotopy invariance, we established a theory of `reciprocity presheaves', which is expected to become a foundation for an extended motive theory encompassing non-homotopy invariant objects.

Free Research Field

数物系科学