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Geometrization of the local Langlands correspondence

Research Project

Project/Area Number 18H01109
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionThe 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
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥16,770,000 (Direct Cost: ¥12,900,000、Indirect Cost: ¥3,870,000)
Fiscal Year 2021: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2020: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2019: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2018: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
KeywordsLanglands 対応 / 整数論 / 代数学 / 局所 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.

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.

Report

(5 results)
  • 2022 Final Research Report ( PDF )
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (7 results)

All 2021 2020 2019 2018 Other

All Int'l Joint Research (1 results) Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 3 results) Presentation (1 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Int'l Joint Research] University of Oregon/University of Michigan(米国)

    • Related Report
      2019 Annual Research Report
  • [Journal Article] Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations II: wild case2021

    • Author(s)
      Imai Naoki、Tsushima Takahiro
    • Journal Title

      Mathematische Annalen

      Volume: 380 Issue: 1-2 Pages: 751-788

    • DOI

      10.1007/s00208-020-02106-1

    • Related Report
      2021 Annual Research Report 2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Automorphic vector bundles on the stack of G-zips2021

    • Author(s)
      Imai, N., Koskivirta, J.-S.
    • Journal Title

      Forum of Mathematics, Sigma

      Volume: 9 Pages: 0-31

    • DOI

      10.1017/fms.2021.32

    • Related Report
      2021 Annual Research Report 2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Potentially good reduction loci of Shimura varieties2020

    • Author(s)
      Naoki Imai and Yoichi Mieda
    • Journal Title

      Tunisian Journal of Mathematics

      Volume: 2 Issue: 2 Pages: 399-454

    • DOI

      10.2140/tunis.2020.2.399

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations I: tame case2019

    • Author(s)
      Naoki Imai and Takahiro Tsushima
    • Journal Title

      International Mathematics Research Notices

      Volume: 印刷中 Pages: 8251-8291

    • DOI

      10.1093/imrn/rny229

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Local Jacquet-Langlands correspondences for simple supercuspidal representations2018

    • Author(s)
      Naoki Imai and Takahiro Tsushima
    • Journal Title

      Kyoto J. Math.

      Volume: 58 Pages: 623-638

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Presentation] Deligne-Lusztig stack2019

    • Author(s)
      Naoki Imai
    • Organizer
      International Conference on Arithmetic Geometry, In honor of Michael Rapoport's 71st birthday
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited

URL: 

Published: 2018-04-23   Modified: 2024-01-30  

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