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Research on Galois representations by local methods

Research Project

Project/Area Number 23740013
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionThe University of Tokyo (2013)
Kyoto University (2011-2012)

Principal Investigator

IMAI Naoki  東京大学, 数理(科)学研究科(研究院), 准教授 (90597775)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
KeywordsGalois 表現
Research Abstract

We studied a geometric realization of the local Langlands correspondence.
More specifically, we constructed a family of affinoids in the Lubin-Tate perfectoid space, which is a limit space of Lubin-Tate spaces, and proved that the cohomology of the reductions realizes the local Langlands correspondence and the local Jacquet-Langlands correspondence for the epipelagic representations in the tame case.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (36 results)

All 2014 2013 2012 2011 Other

All Journal Article (10 results) (of which Peer Reviewed: 2 results) Presentation (26 results) (of which Invited: 2 results)

  • [Journal Article] Action of Hecke operators on cohomology of modular curves of level two2013

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

      Math. Z.

      Volume: 273, no.3-4 Pages: 1139-1159

    • Related Report
      2013 Annual Research Report 2013 Final Research Report 2012 Research-status Report
  • [Journal Article] Toroidal compactifications of Shimura varieties of PEL type and its application2013

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

      RIMS Kokyuroku Bessatsu

      Volume: B44 Pages: 3-24

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] On the connected components of moduli spaces of Kisin modules2012

    • Author(s)
      Naoki Imai
    • Journal Title

      J. Algebra

      Volume: 349, no.1 Pages: 1-7

    • NAID

      120003573893

    • Related Report
      2013 Final Research Report
  • [Journal Article] Dimensions of moduli spaces of finite flat models, Galois-Teichmuller Theory and Arithmetic Geometry2012

    • Author(s)
      Naoki Imai
    • Journal Title

      Adv. Stud. Pure Math.

      Volume: 63 Pages: 251-262

    • Related Report
      2013 Final Research Report
  • [Journal Article] On the connected components of moduli spaces of Kisin modules2012

    • Author(s)
      Naoki Imai
    • Journal Title

      Journal of Algebra

      Volume: 349 Issue: 1 Pages: 1-7

    • DOI

      10.1016/j.jalgebra.2011.09.031

    • NAID

      120003573893

    • Related Report
      2012 Research-status Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Dimensions of moduli spaces of finite flat models2012

    • Author(s)
      Naoki Imai
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 63 Pages: 251-262

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Ramification and moduli spaces of finite flat models2011

    • Author(s)
      Naoki Imai
    • Journal Title

      Ann. Inst. Fourier

      Volume: 61, no.5 Pages: 1943-1975

    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Journal Article] Filtered modules corresponding to potentially semi-stable representations2011

    • Author(s)
      Naoki Imai
    • Journal Title

      J. Number Theory

      Volume: 131, no.2 Pages: 239-259

    • NAID

      120002661522

    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Journal Article] Cohomology of rigid curves with semi-stable coverings

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

      Asian J. Math.

      Volume: (to appear)

    • Related Report
      2013 Final Research Report
  • [Journal Article] Explicit construction of semi-stable models of Lubin-Tate curves with low level

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

      RIMS Kokyuroku Bessatsu

      Volume: (to appear)

    • Related Report
      2013 Final Research Report
  • [Presentation] Good reduction of affinoids for epipelagic representations in the Lubin-Tate perfectoid space2014

    • Author(s)
      Naoki Imai
    • Organizer
      Arithmetic and Algebraic Geometry 2014
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2014-01-29
    • Related Report
      2013 Final Research Report
  • [Presentation] Good reduction of affinoids for epipelagic representations in the Lubin-Tate perfectoid space2014

    • Author(s)
      Naoki Imai
    • Organizer
      Arithmetic and Algebraic Geometry 2014
    • Place of Presentation
      東京大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Good reduction of affinoids for epipelagic representations in the Lubin-Tate perfectoid space2013

    • Author(s)
      Naoki Imai
    • Organizer
      Conference on Local Langlands Conjecture and Galois Representations
    • Place of Presentation
      TATA Institute of Fundamental Research
    • Year and Date
      2013-12-30
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] p進 Langlands対応2013

    • Author(s)
      今井直毅
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-12-12
    • Related Report
      2013 Final Research Report
  • [Presentation] 局所Langlands対応とLubin-Tateパーフェクトイド空間2013

    • Author(s)
      今井直毅
    • Organizer
      談話会
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2013-12-06
    • Related Report
      2013 Final Research Report
  • [Presentation] Lubin-Tate perfectoid空間とモジュラー曲線の半安定モデル2013

    • Author(s)
      今井直毅
    • Organizer
      p可除群とそのモジュライに関する最近の進展
    • Place of Presentation
      京都大学
    • Year and Date
      2013-05-11
    • Related Report
      2013 Final Research Report
  • [Presentation] 半完全環上の Dieudonne理論2013

    • Author(s)
      今井直毅
    • Organizer
      p可除群とそのモジュライに関する最近の進展
    • Place of Presentation
      京都大学
    • Year and Date
      2013-05-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Stable models of Lubin-Tate curves with level three2013

    • Author(s)
      Naoki Imai
    • Organizer
      Automorphic Functions and Arithmetic Geometry : A symposium for Prof. L. Lafforgue's visit
    • Place of Presentation
      九州大学
    • Year and Date
      2013-04-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Good reduction of ramified affinoids in the Lubin-Tate perfectoid space2013

    • Author(s)
      Naoki Imai
    • Organizer
      東京北京パリ数論幾何セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2013-04-24
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Potentially good reduction loci of Shimura varieties2013

    • Author(s)
      Naoki Imai
    • Organizer
      Korea-Japan Joint Seminar on Number Theory and Related Topics
    • Place of Presentation
      梨花女子大学校
    • Year and Date
      2013-01-23
    • Related Report
      2013 Final Research Report
  • [Presentation] Good reduction of ramified affinoids in the Lubin-Tate perfectoid space2013

    • Author(s)
      Naoki Imai
    • Organizer
      Workshop on Modular forms and Galois representations
    • Place of Presentation
      Korea Institute for Advanced Study
    • Year and Date
      2013-01-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Breuil windowの理論2013

    • Author(s)
      今井直毅
    • Organizer
      数論幾何学セミナー
    • Place of Presentation
      北海道大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Stable models of Lubin-Tate curves with level three2013

    • Author(s)
      Naoki Imai
    • Organizer
      Automorphic Functions and Arithmetic Geometry: A symposium for Prof. L. Lafforgue's visit
    • Place of Presentation
      九州大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Local moduli of p-divisible groups2012

    • Author(s)
      Naoki Imai
    • Organizer
      Workshop on Geometrical perspective of topological modular forms
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2012-11-16
    • Related Report
      2013 Final Research Report
  • [Presentation] Lubin-Tate perfectoid space in positive characteristic2012

    • Author(s)
      Naoki Imai
    • Organizer
      玉原数論幾何研究集会
    • Place of Presentation
      玉原国際セミナーハウス
    • Year and Date
      2012-10-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Potentially good reduction loci of Shimura varieties2012

    • Author(s)
      Naoki Imai
    • Organizer
      Symposium on Arithmetic Geometry
    • Place of Presentation
      九州大学
    • Year and Date
      2012-10-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Geometric realization of the local Langlands correspondence for representations of conductor three2012

    • Author(s)
      Naoki Imai
    • Organizer
      Workshop on the arithmetic geometry of Shimura varieties, representation theory, and related topics
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-07-18
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] Cohomology of crystalline loci of open Shimura varieties of PEL type2012

    • Author(s)
      Naoki Imai
    • Organizer
      東京数論幾何週間
    • Place of Presentation
      東京大学
    • Year and Date
      2012-06-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Representations of conductor three in cohomology of Lubin-Tate spaces of height two2012

    • Author(s)
      Naoki Imai
    • Organizer
      Workshop on p-adic arithmetic geometry and motives
    • Place of Presentation
      東北大学
    • Year and Date
      2012-01-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Representations of conductor three in cohomology of Lubin-Tate spaces of height two2012

    • Author(s)
      Naoki Imai
    • Organizer
      Workshop on p-adic arithmetic geometry and motives(招待講演)
    • Place of Presentation
      東北大学
    • Related Report
      2011 Research-status Report
  • [Presentation] PEL型開志村多様体のコンパクト台コホモロジーと隣接輪体コホモロジー2011

    • Author(s)
      今井直毅
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-11-29
    • Related Report
      2013 Final Research Report
  • [Presentation] Dimensions of moduli spaces of finite flat models2011

    • Author(s)
      Naoki Imai
    • Organizer
      The Third PanAsian Number Theory Conference
    • Place of Presentation
      Chinese Academy of Sciences
    • Year and Date
      2011-08-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Cohomology of rigid curves with semi-stable coverings2011

    • Author(s)
      Naoki Imai
    • Organizer
      Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces
    • Place of Presentation
      京都大学
    • Year and Date
      2011-07-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Cohomology of rigid curves with semi-stable coverings2011

    • Author(s)
      Naoki Imai
    • Organizer
      Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces(招待講演)
    • Place of Presentation
      京都大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Dimensions of moduli spaces of finite flat models2011

    • Author(s)
      Naoki Imai
    • Organizer
      The Third PanAsian Number Theory Conference(招待講演)
    • Place of Presentation
      Chinese Academy of Sciences (中国)
    • Related Report
      2011 Research-status Report
  • [Presentation] PEL 型開志村多様体のコンパクト台コホモロジーと隣接輪体コホモロジー2011

    • Author(s)
      今井直毅
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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