L-functions and motivic cohomology of arithmetic varieties and applications to cyclotomic fields

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400007
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba University
• Principal Investigator: Otsubo Noriyuki 千葉大学, 大学院理学研究院, 准教授 (60332566)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: モチーフ / L関数 / モチーフ的コホモロジー / 超幾何関数

Outline of Final Research Achievements

We studied relations between L-functions of arithmetic varieties and their applications to cyclotomic fields. In particular, we obtained new relations between special values of Hecke L-functions of cyclotomic fields and motivic cohomology of Fermat motives, in terms of generalized hypergeometric functions. On the other hand, we defined a new class of families of varieties called hypergeometric fibrations, and for such families, proved the Gross-Deligne conjecture on periods and expressed the regulators in terms of generalized hypergeometric functions. Moreover, we determined the structure of the profinite homology of the tower of Fermat curves, and by using this, gave a simple construction of Ihara-Anderson's universal measure of Jacobi sums.

Free Research Field

数論幾何学