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Motivic cohomology over discrete valuation rings

Research Project

Project/Area Number 23340004
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionRikkyo University (2015)
Nagoya University

Principal Investigator

Geisser Thomas  立教大学, 理学部, 教授 (30571963)

Co-Investigator(Renkei-kenkyūsha) Hesselholt Lars  名古屋大, 多元数理科学研究科, 教授 (10436991)
Saito Shuji  東京工業大学, 学部, 教授 (50153804)
Sato Kanetomo  中央大学, 理工学部数学科, 教授 (50324398)
Asakura Masanori  北海道大学, 理学院数学専攻, 教授 (60322286)
Project Period (FY) 2011-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥17,680,000 (Direct Cost: ¥13,600,000、Indirect Cost: ¥4,080,000)
Fiscal Year 2015: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2011: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Keywordsモチビック・コホモロジー / ススリンホモロジー / スキームの類対論 / テート・ポアテュー双対性 / Motivic Cohomology / Class field theory / ススリン・ホモロジー / 多様体の類体論 / Rojtmanの定理 / テーム基本群 / 類体論 / 代数的サイクル
Outline of Final Research Achievements

Arithmetic geometry is the study of integral or rational solutions of systems of polynomial equations. For this, it is often useful to study the solutions in other domains, like complex number, real numbers, finite fields, or p-adic fields. An important invariant of such solution sets are motivic cohomology, higher Chow groups, and Suslin homology. During this project, I studied these invariants, and proved several interesting results about them.

Report

(6 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • Research Products

    (31 results)

All 2016 2015 2014 2012 2011 Other

All Int'l Joint Research (1 results) Journal Article (10 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 10 results,  Acknowledgement Compliant: 5 results,  Open Access: 1 results) Presentation (16 results) (of which Int'l Joint Research: 3 results,  Invited: 14 results) Remarks (3 results) Funded Workshop (1 results)

  • [Int'l Joint Research] ハイデルベルク大学(ドイツ)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Tame class field theory for singular varieties over algebraically closed fields2016

    • Author(s)
      Thomas Geisser, Alexander Schmidt
    • Journal Title

      Documenta Mathematica

      Volume: 21 Pages: 91-123

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Tame class field theory for singular varieties over finite fields2016

    • Author(s)
      Thomas Geisser. Alexander Schmidt
    • Journal Title

      European Journal of Mathematics

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Rojtman's theorem for normal schemes2015

    • Author(s)
      Thomas Geisser
    • Journal Title

      Mathematical Research Letters

      Volume: 22 Issue: 4 Pages: 1129-1144

    • DOI

      10.4310/mrl.2015.v22.n4.a8

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] モチビック・コホモロジー,その応用と重要な予想2015

    • Author(s)
      Thomas Geisser
    • Journal Title

      数学

      Volume: 67 Pages: 225-245

    • NAID

      130006029674

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parshin's conjecture and motivic cohomology with compact support2015

    • Author(s)
      Thomas Geisser
    • Journal Title

      COMMENTARII MATHEMATICI UNIVERSITATIS SANCTI PAULI

      Volume: 64 (2) Pages: 95-107

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Homological descent for motivic homology theories,2014

    • Author(s)
      Thomas Geisser
    • Journal Title

      Homology, homotopy and applications

      Volume: 2 Issue: 2 Pages: 33-43

    • DOI

      10.4310/hha.2014.v16.n2.a2

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Duality for Z-constructible sheaves on curves over finite fields2012

    • Author(s)
      T.Geisser
    • Journal Title

      Documenta Math.

      Volume: 17 Pages: 989-1002

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a conjecture of Vorst2012

    • Author(s)
      T.Geisser, L.Hesselholt
    • Journal Title

      Math. Zeitschrift

      Volume: 270 Issue: 1-2 Pages: 445-452

    • DOI

      10.1007/s00209-010-0806-2

    • Related Report
      2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite generation conjectures for motivic cohomology theories over finite fields.2012

    • Author(s)
      T.Geisser
    • Journal Title

      Contemp. Math.,

      Volume: 571 Pages: 153-165

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On relative and birelative algebraic K-theory of ring of finite characteristic2011

    • Author(s)
      T.Geisser, L.Hesselholt
    • Journal Title

      Journal American Math.Soc.

      Volume: 24 Issue: 1 Pages: 29-49

    • DOI

      10.1090/s0894-0347-2010-00682-0

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Etale motivic cohomology2016

    • Author(s)
      Thomas Geisser
    • Organizer
      Colloquium on K-theory
    • Place of Presentation
      Mumbai (インド)
    • Year and Date
      2016-01-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Duality for varieties over global fields2015

    • Author(s)
      Thomas Geisser
    • Organizer
      Regulators in Niseko
    • Place of Presentation
      Niseko (北海道)
    • Year and Date
      2015-09-09
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Duality for varieties over global fields2015

    • Author(s)
      Thomas Geisser
    • Organizer
      K-theory, Cyclic Homology and Motives, Weibel's 65th
    • Place of Presentation
      Rutgers University (米国)
    • Year and Date
      2015-08-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] K-theory, TC and logarithmic de Rham-Witt2015

    • Author(s)
      Thomas Geisser
    • Organizer
      Summer School on Algebraic K-theory and Trace Methods
    • Place of Presentation
      Regensburg (ドイツ)
    • Year and Date
      2015-08-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Duality between mod m and m-torsion of etale motivic cohomology2014

    • Author(s)
      Thomas Geisser
    • Organizer
      Workshop on motives
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2014-12-19
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Duality for Z-constructible sheaves on curres over finite fields2012

    • Author(s)
      T.Geisser
    • Organizer
      Algebraic Cycles and L-functions
    • Place of Presentation
      ドイツRegensburg(招待講演)
    • Year and Date
      2012-03-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] Rational K-theory in characteristic p2011

    • Author(s)
      T.Geisser
    • Organizer
      New directions in algebraic K-theory
    • Place of Presentation
      ドイツOberwolfach(招待講演)
    • Year and Date
      2011-05-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] Duality and class field theory

    • Author(s)
      Thomas Geisser
    • Organizer
      Conference on Homotopical Methods in Algebraic Geometry
    • Place of Presentation
      USC Los Angeles
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Higher class field theory for schemes over finite fields

    • Author(s)
      Thomas Geisser
    • Organizer
      Conference on Global Fields
    • Place of Presentation
      Moscow
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Tame class field theory of singular schemes

    • Author(s)
      Thomas Geisser
    • Organizer
      Workshop on Reciprocity Sheaves
    • Place of Presentation
      Yatsugatake
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Class field theory over algebraically closed fields

    • Author(s)
      Thomas Geisser
    • Organizer
      九州代数的数論
    • Place of Presentation
      九州大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Class field theory of singular schemes

    • Author(s)
      Thomas Geisser
    • Organizer
      Conference in honor of Uwe Jannsen's 60th birthday
    • Place of Presentation
      Universitaet Regensburg
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Rojtman's theorem for normal schemes"

    • Author(s)
      Thomas Geisser
    • Organizer
      Conference on motivic and etale homotopy theory
    • Place of Presentation
      Universitaet Heidelberg
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Modulo p motivic cohomology theories

    • Author(s)
      T.Geisser
    • Organizer
      Cycles, motives and homotopy theory
    • Place of Presentation
      Essen (Germany)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Rational motivic theories in characteristic p

    • Author(s)
      T.Geisser
    • Organizer
      Algebraic K-theory and arithmetic
    • Place of Presentation
      Bedlewo (Poland)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Suslin homology, Albanese, and Rojtman's theorem

    • Author(s)
      T.Geisser
    • Organizer
      Algebraic Number theory
    • Place of Presentation
      京都
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Remarks] Tame Class Field Theory for Sing. Varieties

    • URL

      http://arxiv.org/abs/1309.4068

    • Related Report
      2013 Annual Research Report
  • [Remarks] Homological Descent for Motivic Homology Theories

    • URL

      http://arxiv.org/abs/1401.7775

    • Related Report
      2013 Annual Research Report
  • [Remarks] Rojtman's theorem for normal schemes

    • URL

      http://arxiv.org/abs/1402.1831

    • Related Report
      2013 Annual Research Report
  • [Funded Workshop] International workshop on motives2016

    • Place of Presentation
      東京大学(東京都目黒区)
    • Year and Date
      2016-02-15
    • Related Report
      2015 Annual Research Report

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Published: 2011-04-06   Modified: 2019-07-29  

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