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Twisted non-abelian Lubin-Tate theory

Research Project

Project/Area Number 15K13424
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionThe University of Tokyo

Principal Investigator

MIEDA Yoichi  東京大学, 大学院数理科学研究科, 准教授 (70526962)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords局所ラングランズ対応 / 非可換ルビン・テイト理論 / リジッド幾何 / Arthur分類
Outline of Final Research Achievements

For a quadratic extension E/F of p-adic fields which is at worst tamely ramified, we constructed a new automorphism called the ``twisting operator'' on the Lubin-Tate space for GL(n,E). By combining the previously known fact that the etale cohomology of the Lubin-Tate space realizes the local Langlands correspondence for GL(n,E) and the analysis of the action of the twisting operator on the etale cohomology, we obtained a method of determining the parity of the L-parameter of a conjugate self-dual irreducible supercuspidal representation of GL(n,E).

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (6 results)

All 2018 2017 2016 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (4 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results) Remarks (1 results)

  • [Journal Article] Arthur分類とその応用2018

    • Author(s)
      三枝 洋一
    • Journal Title

      RIMS講究録別冊「代数的整数論とその周辺2016」

      Volume: 未定

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] パーフェクトイド代数の概要2017

    • Author(s)
      三枝 洋一
    • Organizer
      可換環論と数論幾何の新展開 --- ホモロジカル予想を通じて
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 局所Gan-Gross-Prasad予想について2017

    • Author(s)
      三枝 洋一
    • Organizer
      倉敷整数論集会2017
    • Related Report
      2017 Annual Research Report
  • [Presentation] Arthur分類とその応用2016

    • Author(s)
      三枝 洋一
    • Organizer
      代数的整数論とその周辺2016
    • Place of Presentation
      京都大学
    • Year and Date
      2016-12-01
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Parity of the Langlands parameters of conjugate self-dual representations of GL(n) and the local Jacquet-Langlands correspondence2016

    • Author(s)
      三枝 洋一
    • Organizer
      Japan-Taiwan Joint Conference on Number Theory 2016
    • Place of Presentation
      National Taiwan University(台湾)
    • Year and Date
      2016-09-10
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] 三枝洋一のウェブサイト

    • URL

      http://www.ms.u-tokyo.ac.jp/~mieda/index-j.html

    • Related Report
      2017 Annual Research Report 2016 Research-status Report 2015 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2019-03-29  

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