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Various problems in arithmetic geometry concerning the structure elucidation of arithmetic fundamental groups

Research Project

Project/Area Number 22340006
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKyoto University

Principal Investigator

TAMAGAWA Akio  京都大学, 数理解析研究所, 教授 (00243105)

Research Collaborator RASMUSSEN Christopher  
CADORET Anna  
SAIDI Mohamed  
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥11,180,000 (Direct Cost: ¥8,600,000、Indirect Cost: ¥2,580,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2010: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Keywords代数曲線 / 被覆 / 基本群 / ガロア表現 / アーベル多様体 / 正標数 / 国際研究者交流 / 米国:仏国:英国:台湾 / 米国:仏国:英国:伊国:台湾 / 米国:仏国:英国:スペイン / 米国:仏国:英国:独国
Outline of Final Research Achievements

As the original research plans, I invited each of my three overseas collaborators -- Christopher Rasmussen, Anna Cadoret and Mohamed Saidi -- almost every year during the period, by means of the present kakenhi grant and other financial sources, and made sufficient research achievements on the arithmetic geometry of covers and fundamental groups of algebraic curves. During the period, I submitted two joint papers with Rasmussen and had one more in preparation; published six joint papers with Cadoret and submitted three more; and published one joint paper with Saidi, had one more to appear, submitted two more and had one more in preparation.

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (25 results)

All 2015 2014 2013 2012 2011 2010 Other

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (11 results) (of which Invited: 9 results) Remarks (5 results)

  • [Journal Article] Controlling the Galois images in one-dimensional families of l-adic representations2014

    • Author(s)
      Anna Cadoret and Akio Tamagawa
    • Journal Title

      Journal of Algebra

      Volume: 412 Pages: 189-206

    • DOI

      10.1016/j.jalgebra.2014.04.024

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Note on torsion conjecture2013

    • Author(s)
      Anna Cadoret and Akio Tamagawa
    • Journal Title

      Seminaires et Congres

      Volume: 27 Pages: 57-68

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A uniform open image theorem for l-adic representations II2013

    • Author(s)
      Anna Cadoret and Akio Tamagawa
    • Journal Title

      Duke Mathematical Journal

      Volume: 未定

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A uniform open image theorem for l-adic representations I2012

    • Author(s)
      Anna Cadoret and Akio Tamagawa
    • Journal Title

      Duke Mathematical Journal

      Volume: 161 Issue: 13 Pages: 2605-2634

    • DOI

      10.1215/00127094-1812954

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniform boundedness of p-primary torsion of abelian schemes2012

    • Author(s)
      Anna Cadoret and Akio Tamagawa
    • Journal Title

      Inv. Math.

      Volume: 2011;188, no.1 Issue: 1 Pages: 83-125

    • DOI

      10.1007/s00222-011-0343-6

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Note on torsion conjecture2012

    • Author(s)
      Anna Cadoret, Akio Tamagawa
    • Journal Title

      Seminaires et Congres

      Volume: 27(印刷中) Pages: 57-68

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Hom-form of Grothendieck's birational anabelian conjecture in characteristic p>02011

    • Author(s)
      Mohamed Saidi, Akio Tamagawa
    • Journal Title

      Algebra and Number Theory

      Volume: 5 Issue: 2 Pages: 131-184

    • DOI

      10.2140/ant.2011.5.131

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a weak variant of the geometric torsion conjecture2011

    • Author(s)
      Anna Cadoret, Akio Tamagawa
    • Journal Title

      Journal of Algebra

      Volume: 346 Issue: 1 Pages: 227-247

    • DOI

      10.1016/j.jalgebra.2011.09.002

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A uniform open image theorem for S¥ell$-adic representations I

    • Author(s)
      Anna Cadoret, Akio Tamagawa
    • Journal Title

      Duke Mathematical Journal

      Volume: (掲載確定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Uniform boundedness of torsion of abelian varieties and Galois representations (joint work with Anna Cadoret)2015

    • Author(s)
      Akio Tamagawa
    • Organizer
      TIMS Taipei Number Theory Seminar
    • Place of Presentation
      National Taiwan University
    • Year and Date
      2015-03-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] A finiteness conjecture for abelian varieties over number fields (joint work with Christopher Rasmussen)2015

    • Author(s)
      Akio Tamagawa
    • Organizer
      NCTS Number Theory Seminar
    • Place of Presentation
      National Tsing Hua University
    • Year and Date
      2015-03-25
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Survey on anabelian geometry in positive characteristic2010

    • Author(s)
      Mohamed Saidi, Akio Tamagawa
    • Organizer
      The 3rd MSJ-SI "Developments of Galois-Teichmueller theory and anabelian geometry"
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Representations of etale fundamental groups and applications(joint work with Anna Cadoret)2010

    • Author(s)
      Akio Tamagawa
    • Organizer
      The Second PanAsian Number Theory Conference(PANT-Kyoto 2010)
    • Place of Presentation
      京都大学数理解析研究所(招待講演)
    • Year and Date
      2010-09-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Arithmetic of abelian varieties over function fields and an application to anabelian geometry (joint work with Mohamed Saidi)

    • Author(s)
      Akio Tamagawa
    • Organizer
      Fundamental Groups in Arithmetic and Algebraic Geometry
    • Place of Presentation
      Centro di Ricerca Matematica Ennio De Giorgi (イタリア)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Uniform boundedness and arithmetic fundamental groups

    • Author(s)
      Akio Tamagawa
    • Organizer
      Barcelona-Boston-Tokyo Number Theory Seminar in Memory of Fumiyuki Momose
    • Place of Presentation
      Universitat Polit\`ecnica de Catalunya (スペイン)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Variation of $l$-adic Galois representations (joint work with Anna Cadoret)

    • Author(s)
      Akio Tamagawa
    • Organizer
      Arithmetic Geometry week in Tokyo
    • Place of Presentation
      Universit\'e Bordeaux 1 (フランス)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Variation of fundamental groups of curves in positive characteristic

    • Author(s)
      Akio Tamagawa
    • Organizer
      Conference on Galois covers and deformations
    • Place of Presentation
      東京大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] モジュラー曲線と楕円曲線

    • Author(s)
      玉川安騎男
    • Organizer
      第58回Encounter with Mathematics「Modular曲線の数論と幾何--その魅力と百瀬さんの足跡と--」
    • Place of Presentation
      中央大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] アーベル多様体の有理ねじれ点の普遍上界とガロア表現(Anna Cadoret氏との共同研究)

    • Author(s)
      玉川安騎男
    • Organizer
      豊田中研数学コロキウム
    • Place of Presentation
      豊田中央研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 有限体上の代数曲線の遠アーベル幾何の精密化について(Mohamed Saidi氏との共同研究)

    • Author(s)
      玉川安騎男
    • Organizer
      豊田中研数学コロキウム
    • Place of Presentation
      豊田中央研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Remarks] 京都大学数理解析研究所

    • URL

      http://www.kurims.kyoto-u.ac.jp/ja/list/tamagawa.html

    • Related Report
      2014 Annual Research Report
  • [Remarks] 京都大学数理解析研究所

    • URL

      http://www.kurims.kyoto-u.ac.jp/ja/list/tamagawa.html

    • Related Report
      2013 Annual Research Report
  • [Remarks] 京都大学数理解析研究所

    • URL

      http://www.kurims.kyoto-u.ac.jp/ja/list/tamagawa.html

    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://www.kurims.kyoto-u.ac.jp/ja/list/tamagawa.html

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.kurims.kyoto-u.ac.jp/ja/list/tamagawa.html

    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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