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Research on p-adic Hodge theory with arithmetic D-modules

Research Project

Project/Area Number 21540008
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionThe University of Tokyo

Principal Investigator

TSUJI Takeshi  東京大学, 大学院・数理科学研究科, 教授 (40252530)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsp進Hodge理論 / 数論的D加群 / p進perverse層
Research Abstract

Takeshi Tsuji studied p-adic Hodge theory for p-adic perverse sheaves on a poper smooth algebraic variety with good reduction over a p-adic field, and generalized the notion of crystalline sheaves for local systems to perverse sheaves whose singular locus lies on a simple normal crossing divisor. He also studied the weight spectral sequence of p-adic cohomology constructed from nearby cycles D-modules, and proved its functoriality and its compatibility with duality, Frobenius automorphisms, and algebraic correspondences.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (18 results)

All 2011 2010 2009

All Journal Article (7 results) (of which Peer Reviewed: 5 results) Presentation (11 results)

  • [Journal Article] Purity for Hodge-Tate representations2011

    • Author(s)
      T. Tsuji
    • Journal Title

      Mathematische Annalen

      Volume: 350 Issue: 4 Pages: 829-866

    • DOI

      10.1007/s00208-010-0582-7

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] p-adic perverse sheaves and filtered arithmetic D-modules with singularities along a normal crossing divisor, Algebraische Zahlentheorie 20112011

    • Author(s)
      T. Tsuji
    • Journal Title

      Mathematisches Forschungsinstitut Oberwolfach Report

      Volume: 31 Pages: 1735-1738

    • Related Report
      2011 Final Research Report
  • [Journal Article] p-adic perverse sheaves and arithmetic D-modules with singularities along a normal crossing divisor2011

    • Author(s)
      辻雄
    • Journal Title

      Algebraische Zahlentheorie 2011, Mathematisches Forschungsinstitut Oberwolfach Report

      Volume: 31 Issue: 2 Pages: 1735-1738

    • DOI

      10.4171/owr/2011/31

    • Related Report
      2011 Annual Research Report
  • [Journal Article] On the de Rham and p-adic realizations of the elliptic polylogarithm for CM elliptic curves, Annales Scientifiques de l' ENS 432010

    • Author(s)
      K. Bannai, S. Kobayashi and T. Tsuji
    • Journal Title

      fascicule

      Volume: 2 Pages: 185-234

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On nearby cycles and D-modules of log schemes incharacteristic p> 02010

    • Author(s)
      T. Tsuji
    • Journal Title

      Compositio Mathematica

      Volume: 146 Issue: 6 Pages: 1552-1616

    • DOI

      10.1112/s0010437x10004768

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the de Rham and p-adic realizations of the elliptic polylogarithm for CM elliptic curves2010

    • Author(s)
      K.Bannai, S.Kobayashi, T.Tsuji
    • Journal Title

      Annales Scientifiques de l'ENS

      Volume: 43 Pages: 185-234

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On nearby cycles and D-modules of log schemes in characteristic p>02010

    • Author(s)
      辻雄
    • Journal Title

      Compositio Mathematica

      Volume: 146 Pages: 1552-1616

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] p-adic perverse sheaves and filtered arithmetic D-modules with singularities along a normal crossing divisor2011

    • Author(s)
      辻雄
    • Organizer
      Algebraische Zahlentheorie, Mathematisches Forschungsinstitut Oberwolfach
    • Place of Presentation
      Germany
    • Year and Date
      2011-06-22
    • Related Report
      2011 Final Research Report
  • [Presentation] p-adic perverse sheaves and arithmetic D-modules with singularitiesalong a normal crossing divisor2011

    • Author(s)
      辻雄
    • Organizer
      Algebraische Zahlentheorie 2011
    • Place of Presentation
      Mathematisches Forschung sinstitut Oberwolfach,ドイツ(招待講演)
    • Year and Date
      2011-06-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] p-adic perverse sheaves and arithmetic D-modules on a curve2010

    • Author(s)
      辻雄
    • Organizer
      Arithmetic geometry and p-adic differential equations
    • Place of Presentation
      東北大学
    • Year and Date
      2010-07-02
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Semi-stable reduction and arithmetic D-modules, Current trends in logarithmic geometry2010

    • Author(s)
      辻雄
    • Organizer
      Universite Bordeaux 1
    • Place of Presentation
      France
    • Year and Date
      2010-06-24
    • Related Report
      2011 Final Research Report
  • [Presentation] Semi-stable reduction and arithmetic D-modules, Current trends in logarithmic geometry2010

    • Author(s)
      辻雄
    • Organizer
      Current trends in logarithmic geometry
    • Place of Presentation
      Universite Bordeauxフランス
    • Year and Date
      2010-06-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] p-adic perverse sheaves and arithmetic D-modules on a curve2010

    • Author(s)
      辻雄
    • Organizer
      Conference de Geometrie Arithmetiqueen l'honneur de Jean-Marc Fontaine
    • Place of Presentation
      アンリ・ポワンカレ研究所(フランス・パリ)
    • Year and Date
      2010-03-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] p-adic perverse sheaves and arithmetic D-modules on a curve2010

    • Author(s)
      辻雄
    • Organizer
      Conference de Geometrie Arithmetique en l' honneur de Jean-Marc Fontaine, Institute Henri Poincare
    • Place of Presentation
      France
    • Related Report
      2011 Final Research Report
  • [Presentation] Nearby cycles and D-modules of log schemes in characteristic p> 02009

    • Author(s)
      辻雄
    • Organizer
      East Asia Number Theory Conference
    • Place of Presentation
      清華大学,中国
    • Year and Date
      2009-08-20
    • Related Report
      2011 Final Research Report
  • [Presentation] Nearby cycles and D-modules of log schemes in characteristic p>02009

    • Author(s)
      辻雄
    • Organizer
      East Asia Number Theory Conference
    • Place of Presentation
      清華大学(中国・北京)
    • Year and Date
      2009-08-20
    • Related Report
      2009 Annual Research Report
  • [Presentation] Arithmetic D-modules and weight spectral sequences, Journees de Geometrie Arithmetique de Rennes2009

    • Author(s)
      辻雄
    • Organizer
      Institut de Recherche Mathematique de Rennes
    • Place of Presentation
      France
    • Year and Date
      2009-07-07
    • Related Report
      2011 Final Research Report
  • [Presentation] Arithmetic D-modules and weight spectral sequences2009

    • Author(s)
      辻雄
    • Organizer
      Journees de Geometrie Arithmetique de Rennes
    • Place of Presentation
      レンヌ数学研究所(フランス・レンヌ)
    • Year and Date
      2009-07-07
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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