Strategic research to construct motivic units using new symmetry
About this project
- Japan Grant Number
- JP18H05233
- Funding Program
- Grants-in-Aid for Scientific Research
- Funding organization
- Japan Society for the Promotion of Science
- Project/Area Number
- 18H05233
- Research Category
- Grant-in-Aid for Scientific Research (S)
- Allocation Type
-
- Single-year Grants
- Review Section / Research Field
-
- Broad Section B
- Research Institution
-
- Keio University
- Project Period (FY)
- 2018-06-11 〜 2023-03-31
- Project Status
- Completed
- Budget Amount*help
- 119,470,000 Yen (Direct Cost: 91,900,000 Yen Indirect Cost: 27,570,000 Yen)
Research Abstract
Our aim was to prospect the construction of motivic units applicable to the proof of conjectures in arithmetic geometry via a motivic object called the polylogarithm. As a concrete objective, we studied the polyogarithm on an algebraic torus associated to a totally real field with equivariant action of the unit group. We discovered the Shintani generating class which universally generates the special balues of the Hecke L-functions of the totally real field. Using a conjectural structure called a plectic structure, we formulate a precise conjecture concerning the equivariant polylogarithm and its relation to the Beilinson conjecture for the Hecke L-function of totally real fields.