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Motive theory based on Weil reciprocity

Research Project

Project/Area Number 24654001
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionTohoku University

Principal Investigator

YAMAZAKI Takao  東北大学, 理学(系)研究科(研究院), 教授 (00312794)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords数論幾何 / モチーフ / 代数学 / 代数的サイクル / 国際研究者交流(フランス) / Weil 相互律
Outline of Final Research Achievements

Celebrated theory of mixed motives, due to Voevodsky, is yet to be extended in order to take into account non-homotopy invariant objects. Indeed, there are fundamental objects, such as relative Picard group of an algebraic curve, that are not homotopy invariant. By taking Weil reciprocity in the place of homotopy invariance, we established a theory of `reciprocity presheaves', which is expected to become a foundation for an extended motive theory encompassing non-homotopy invariant objects.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (18 results)

All 2015 2014 2013 2012 Other

All Journal Article (5 results) (of which Peer Reviewed: 1 results,  Acknowledgement Compliant: 1 results) Presentation (13 results) (of which Invited: 7 results)

  • [Journal Article] Algebraic integrable systems related to spectral curves with automorphisms2015

    • Author(s)
      Rei Inoue, Pol Vanhaecke and Takao Yamazaki
    • Journal Title

      Journal of Geometry and Physics

      Volume: 87 Pages: 198-216

    • DOI

      10.1016/j.geomphys.2014.07.008

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Torsion points on hyperelliptic Jacobians via Anderson's p-adic soliton theory2013

    • Author(s)
      Yuken Miyasaka, Takao Yamazaki
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 36 Pages: 2013-2013

    • Related Report
      2013 Research-status Report 2012 Research-status Report
  • [Journal Article] Voevodsky's motives and Weil reciprocity2013

    • Author(s)
      Bruno Kahn, Takao Yamazaki
    • Journal Title

      Duke Mathematical Journal

      Volume: 162 Pages: 2751-2796

    • Related Report
      2013 Research-status Report
  • [Journal Article] Brauer-Manin pairing, class field theory and motivic homology2013

    • Author(s)
      Takao Yamazaki
    • Journal Title

      Nagoya Mathematical Journal

      Volume: 210 Pages: 29-58

    • Related Report
      2013 Research-status Report 2012 Research-status Report
  • [Journal Article] ヴォエヴォドスキーのモチーフとヴェイユ相互律2013

    • Author(s)
      山崎隆雄
    • Journal Title

      数理解析研究所講究録別冊

      Volume: 44

    • Related Report
      2013 Research-status Report 2012 Research-status Report
  • [Presentation] p-adic soliton theory and arithmetic geometry2014

    • Author(s)
      Takao Yamazaki
    • Organizer
      Novel visage of arithmetic and derived geometry
    • Place of Presentation
      中央大学
    • Year and Date
      2014-10-10
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Reciprocity sheaves2014

    • Author(s)
      Takao Yamazaki
    • Organizer
      Workshop on arithmetic geometry in Hakodate
    • Place of Presentation
      北海道教育大学函館校
    • Year and Date
      2014-05-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Somekawa's K-groups and Voevodsky's Hom groups2012

    • Author(s)
      Takao Yamazaki
    • Organizer
      Arithmetic geometry seminar
    • Place of Presentation
      北海道大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Reciprocity sheaves

    • Author(s)
      Takao Yamazaki
    • Organizer
      Workshop on reciprocity sheaves
    • Place of Presentation
      八ヶ岳自然文化園
    • Related Report
      2013 Research-status Report
  • [Presentation] Reciprocity sheaves: towards non-homotopy invariant motive theory

    • Author(s)
      Takao Yamazaki
    • Organizer
      Arithmetic, differential and geometry
    • Place of Presentation
      東北大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Reciprocity sheaves: towards non-homotopy invariant motive theory

    • Author(s)
      Takao Yamazaki
    • Organizer
      Takao Yamazaki
    • Place of Presentation
      東京大学
    • Related Report
      2013 Research-status Report
  • [Presentation] p-adic soliton theory and torsion points on Jacobian varieties

    • Author(s)
      Takao Yamazaki
    • 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
      2013 Research-status Report
  • [Presentation] p-adic soliton theory and torsion points on Jacobian varieties

    • Author(s)
      Takao Yamazaki
    • Organizer
      East Asia Number Theory Conference
    • Place of Presentation
      九州大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Voevodsky's motives and Weil reciprocity

    • Author(s)
      Takao Yamazaki
    • Organizer
      2014 NCTS Mini-Workshop on Number Theory
    • Place of Presentation
      新竹市,台湾
    • Related Report
      2013 Research-status Report
  • [Presentation] Torsion points on Jacobian varieties via Anderson's p-adic soliton theory

    • Author(s)
      Takao Yamazaki
    • Organizer
      Tohoku-Fudan Workshop
    • Place of Presentation
      東北大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Voevodsky's category of motives and Milnor K-groups attached to semi-abelian varieties

    • Author(s)
      Takao Yamazaki
    • Organizer
      Number Theory Day in Keio
    • Place of Presentation
      慶應義塾大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Torsion points on Jacobian varieties via Anderson's p-adic soliton theory

    • Author(s)
      Takao Yamazaki
    • Organizer
      Seminaire de theorie des nombres
    • Place of Presentation
      フランス,パリ
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Algebraic cycles on a product of curves over a p-adic field

    • Author(s)
      Takao Yamazaki
    • Organizer
      Seminaire autour des cycles algebriques
    • Place of Presentation
      フランス,パリ
    • Related Report
      2012 Research-status Report
    • Invited

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Published: 2013-05-31   Modified: 2019-07-29  

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