Arithmetic geometry of Shimura varieties and non-abelian class field theory

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800013
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Ito Tetsushi 京都大学, 理学研究科, 准教授 (10456840)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 代数学 / 数論幾何学 / 志村多様体

Outline of Final Research Achievements

The purpose of this research is to study the arithmetic geometry of Shimura varieties, and apply it to non-abelian class field theory. For this purpose, I organized several workshops on some topics including automorphic representations of classical groups, the cohomology of locally symmetric spaces, the Langlands correspondences over function fields, periods of automorphic representations, the trace formula, and promoted the study of Shimura varieties and related topics. Moreover, I investigated geometric and combinatorial aspects of Galois representations associated with plane curves, and obtained number theoretic results on the defining equations and symmetries of plane curves. I explicitly calculated the Galois action on 4-torsion points on the Fermat quartic. I investigated applications of geometric properties of orthogonal Shimura varieties to K3 surfaces.

Free Research Field

数論幾何学