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Study on arithmetic geometry by arithmetic cohomology

Research Project

Project/Area Number 20540025
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Denki University

Principal Investigator

NAKAJIMA Yukiyoshi  東京電機大学, 工学部, 教授 (80287440)

Project Period (FY) 2008 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords数論幾何 / p進Steenbrink-Mokrane複体 / Clemens-Schmid系列 / 剛性コホモロジー / p進モノドロミー重み予想 / p進対数強Lefschetz予想 / 分裂単体的半安定多様体 / 層係数p進Steenbrink複体 / 層係数p進Steenbrink系列 / 擬モノドロミー作用素 / 相対Clemens-Schmid系列 / 単数根F-クリスタル / Steenbrink-Mokrane複体 / コホモロジー / 収束トポス / p進純粋性 / 半安定型多様体 / p進重み複体 / p進重み系列 / 基礎対数スキームの系列 / p進Steenbrink重み複体 / p進Steenbrkink重み系列 / E2退化 / p進Steenbrkink-Mokrane重み複体 / 無限小コホモロジー / 兵藤加藤の同型射 / 多様体の分解 / 擬大域チャート / 対数的収束トポス / 重み付き消滅サイクル / 擬態域チャート / 仮想ベッチ数 / 単体的安定多様体
Research Abstract

In arithmetic geometry(=the conjunction of arithmetic andgeometry), there is a theory of p-adic cohomology. For this theory, we have constructed afundamental theory of logarithmic convergent topoi and proved various properties oflogarithmic weight filtration. We have also constructed the p-adic weight spectralsequences of proper varieties with any singularities over the fraction field of a completediscrete valuation ring of mixed characteristics and proved the fundamental properties ofit.

Report

(7 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (20 results)

All 2012 2010 2008 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results) Presentation (14 results) (of which Invited: 2 results) Book (2 results)

  • [Journal Article] 書評 Bernard Le Stum: Rigid Cohomology2012

    • Author(s)
      中島幸喜
    • Journal Title

      雑誌数学

      Pages: 97-101

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weight filtration and slope filtration on the rigid cohomology of a variety in characteristic p > 02012

    • Author(s)
      中島幸喜
    • Journal Title

      Mem. Soc. Math. France

      Volume: 130/131 Pages: 1-264

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 書評Bernard Le Stum : Rigid Cohomology2012

    • Author(s)
      中島幸喜
    • Journal Title

      数学

      Volume: 64 Pages: 97-101

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weight filtration and slopefiltration on the rigid cohomology ofa variety in characteristic p>0

    • Author(s)
      中島幸喜
    • Journal Title

      Memoire de la Societe Mathematique deFrance

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Weight filtration on the logcrystalline cohomology of asemistable scheme and weightfiltration on the infinitesimalcohomology of a proper scheme2012

    • Author(s)
      中島幸喜
    • Organizer
      p-adiccohomology and its applications toarithmetic geometry
    • Place of Presentation
      東北大学
    • Year and Date
      2012-11-29
    • Related Report
      2012 Final Research Report
  • [Presentation] Weight filtration on theinfinitesimal cohomology in mixedcharacteristics2012

    • Author(s)
      中島幸喜
    • Organizer
      ホッジ理論と代数幾何学
    • Place of Presentation
      東京電機大学
    • Year and Date
      2012-02-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Weight filtration on the logcrystalline cohomology of asemistable scheme and weightfiltration on the infinitesimalcohomology of a proper scheme II2012

    • Author(s)
      中島幸喜
    • Organizer
      北海道大学数論幾何学セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-02-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Weight filtration on the log crystalline cohomology of a semistable scheme and weight filtration on the infinitesimal cohomology of a proper scheme II2012

    • Author(s)
      中島幸喜
    • Organizer
      北海道大学数論幾何学セミナー
    • Place of Presentation
      北海道大学(北海道)
    • Year and Date
      2012-02-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] Weight filtration on the logcrystalline cohomology of asemistable scheme and weightfiltration on the infinitesimalcohomology of a proper scheme I2012

    • Author(s)
      中島幸喜
    • Organizer
      北海道大学数論幾何学セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-02-22
    • Related Report
      2012 Final Research Report
  • [Presentation] Weight filtration on the log crystalline cohomology of a semistable scheme and weight filtration on the infinitesimal cohomology of a proper scheme I2012

    • Author(s)
      中島幸喜
    • Organizer
      北海道大学数論幾何学セミナー
    • Place of Presentation
      北海道大学(北海道)
    • Year and Date
      2012-02-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Crystalline construction of p-adic weight-filtered Steenbrink complex and its applications2012

    • Author(s)
      中島幸喜
    • Organizer
      国際会議 p-adic cohomology and its applications to arithmetic geometry
    • Place of Presentation
      東北大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Weight filtration on the log crystalline cohomology of a semistable scheme and weight filtration on the infinitesimal cohomology of a proper scheme2012

    • Author(s)
      中島幸喜
    • Organizer
      ワークショップ「ホッジ理論と代数幾何学」
    • Place of Presentation
      東京電機大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Weight filtrations on log crystalline cohomologies of familiesof split truncated semistablevarieties2010

    • Author(s)
      中島幸喜
    • Organizer
      Mathematique du CNRS
    • Place of Presentation
      ボルドー大学
    • Year and Date
      2010-06-24
    • Related Report
      2012 Final Research Report
  • [Presentation] Weight filtrations on log crystalline cohomologies of families of split truncated semistable varieties2010

    • Author(s)
      中島幸喜
    • Organizer
      Mathematique du CNRS
    • Place of Presentation
      ボルドー大学
    • Year and Date
      2010-06-24
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Weight filtrations on log crystalline cohomologies of families of split truncated semistable varieties2010

    • Author(s)
      中島幸喜
    • Organizer
      Mathematique du CNRS
    • Place of Presentation
      ボルドー大学(フランス)
    • Year and Date
      2010-06-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Comparison theorem between truncated split cosimplicial weight -filtered crystalline complexes and log de Rham-Witt complexes2008

    • Author(s)
      中島幸喜
    • Organizer
      p-adic method and its applications inarithmetic geometryat Sendai
    • Place of Presentation
      東北大学
    • Year and Date
      2008-11-06
    • Related Report
      2012 Final Research Report
  • [Presentation] Comparison theorem betwe en truncated split cosimplicial weightfiltered crystalline complexes and log de Rham-Witt complexes2008

    • Author(s)
      中島幸喜
    • Organizer
      p-adic method and its applications in arithmetic geome try at Sendai
    • Place of Presentation
      東北大学
    • Year and Date
      2008-11-06
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Comparison theorem between truncated split cosimplicial weight-filtered crystalline complexes and log de Rham-Witt complexes2008

    • Author(s)
      Nakkajima, Yukiyoshi
    • Organizer
      p-adic method and its applications in arithmetic geometry at Sendai
    • Place of Presentation
      東北大学
    • Year and Date
      2008-11-06
    • Related Report
      2008 Annual Research Report
  • [Book] Weight filtrations on log crystalline cohomologies of families of open smooth varieties2008

    • Author(s)
      中島幸喜、志甫淳
    • Publisher
      Springer-Verlag
    • Related Report
      2010 Self-evaluation Report
  • [Book] Weight filtrations on log crystalline cohomologies of families of open smooth varieties2008

    • Author(s)
      Nakkajima, Y., Shiho, A.
    • Total Pages
      282
    • Publisher
      Springer-Verlag
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2019-07-29  

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