Geometrization of the local Langlands correspondence

2022 Fiscal Year Final Research Report

• Project/Area Number: 18H01109
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: The University of Tokyo
• Principal Investigator: Imai Naoki 東京大学, 大学院数理科学研究科, 准教授 (90597775)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: Langlands 対応

Outline of Final Research Achievements

Using methods of the geometric Langlands correspondence, we studied the geometric realization of the local Langlands correspondence and the mod p reduction of Shimura varieties. In particular, we showed the Kottwitz conjecture for inner forms of GL(3).We also studied the structure of the moduli space of L-parameters that appears in the geometrization of the local Langlands correspondence.

Free Research Field

数論

Academic Significance and Societal Importance of the Research Achievements

局所 Langlands 対応の幾何学的実現に関して，GL(3) の内部形式に対する Kottwitz 予想を証明することができた．志村多様体の幾何についても，従来の研究では知られていなかった新しい現象を発見することができており，学術的意義があると考えられる．