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Various problems in arithmetic geometry concerning arithmetic fundamental groups and their interrelationships

Research Project

Project/Area Number 15H03609
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)

Project Period (FY) 2015-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥12,870,000 (Direct Cost: ¥9,900,000、Indirect Cost: ¥2,970,000)
Fiscal Year 2019: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2017: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2016: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
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 / 代数学 / 米国:英国:仏国:台湾:中国 / 米国:仏国:英国:オランダ:台湾 / 米国:仏国:英国:ルクセンブルク
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 arithmetic geometry concerning arithmetic fundamental groups. During the period, I published three joint papers with Rasmussen and had one more in preparation; published four joint papers with Cadoret, submitted one more and had four more in preparation; and published four joint papers with Saidi, submitted one more and had three more in preparation.

Academic Significance and Societal Importance of the Research Achievements

本研究は、代数多様体の数論的基本群の群論的及び数論幾何学的構造を解明する、というのが究極の目的であり、そのために、6つの具体的重要問題とその相互関係の究明を目指して研究を行った。3名の海外研究協力者(Christopher Rasmussen、Anna Cadoret、Mohamed Saidi)との3つの共同研究を中核として、これら6つの問題全てに対して多数の重要な知見を得て、研究期間中に計13編の論文を発表、さらに投稿中・準備中の論文も10編以上ある。これらの研究成果を通じて、当該研究分野の進展に大きく貢献できたのとともに、国際研究ネットワークを持続発展させることができた。

Report

(6 results)
  • 2020 Final Research Report ( PDF )
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • Research Products

    (48 results)

All 2019 2018 2017 2016 2015 Other

All Int'l Joint Research (22 results) Journal Article (11 results) (of which Int'l Joint Research: 10 results,  Peer Reviewed: 11 results) Presentation (8 results) (of which Int'l Joint Research: 3 results,  Invited: 5 results) Remarks (5 results) Funded Workshop (2 results)

  • [Int'l Joint Research] Wesleyan University/Colorado State University(米国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Sorbonne Universite(フランス)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Exeter University(英国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Wesleyan University/University of California, Los Angeles(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Sorbonne Universite(フランス)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Exeter University(英国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Academia Sinica(台湾)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Tsinghua University(中国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Wesleyan University(米国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Ecole Polytechnique/Sorbonne Universite(フランス)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Exeter University(英国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] National Tsing Hua University/National Taiwan University(台湾)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Tsinghua University(中国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Wesleyan University/Purdue University(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Ecole Polytechnique(フランス)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Exeter University/Nottingham University(英国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Vrije Universiteit Amsterdam(オランダ)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Academia Sinica(台湾)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Wesleyan University(米国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Ecole Polytechnique(フランス)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Exeter University(英国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] University of Luxembourg(ルクセンブルク)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] On the geometric image of F_l-linear representations of etale fundamental groups2019

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

      International Mathematics Research Notices

      Volume: 2019 Issue: 9 Pages: 2735-2762

    • DOI

      10.1093/imrn/rnx193

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Genus of abstract modular curves with level-l structures2019

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

      Journal fur die reine und angewandte Mathematik (Crelles Journal)

      Volume: 2019 Issue: 752 Pages: 25-61

    • DOI

      10.1515/crelle-2016-0057

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Cyclic covers and Ihara’s question2019

    • Author(s)
      Rasmussen Christopher、Tamagawa Akio
    • Journal Title

      Research in Number Theory

      Volume: 5 Issue: 4 Pages: 1-23

    • DOI

      10.1007/s40993-019-0170-1

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A refined version of Grothendieck’s anabelian conjecture for hyperbolic curves over finite fields2018

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

      Journal of Algebraic Geometry

      Volume: 27 Issue: 3 Pages: 383-448

    • DOI

      10.1090/jag/708

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Specialization of l-adic representations of arithmetic fundamental groups and applications to arithmetic of abelian varieties2018

    • Author(s)
      Akio Tamagawa
    • Journal Title

      Proceedings of Symposia in Pure Mathematics

      Volume: 97.2 Pages: 573-595

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetic of abelian varieties with constrained torsion2017

    • Author(s)
      Christopher Rasmussen, Akio Tamagawa
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 369 Issue: 4 Pages: 2395-2424

    • DOI

      10.1090/tran/6790

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A refined version of Grothendieck's birational anabelian conjecture for curves over finite fields2017

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

      Advances in Mathematics

      Volume: 310 Pages: 610-662

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Abelian surfaces good away from 22017

    • Author(s)
      Christopher Rasmussen, Akio Tamagawa
    • Journal Title

      International Journal of Number Theory

      Volume: 13 Issue: 04 Pages: 991-1001

    • DOI

      10.1142/s179304211750052x

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Geometric monodromy --- semisimplicity and maximality2017

    • Author(s)
      Anna Cadoret, Chun-Yin Hui, Akio Tamagawa
    • Journal Title

      Annals of Mathematics

      Volume: 186 Issue: 1 Pages: 205-236

    • DOI

      10.4007/annals.2017.186.1.5

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Gonality of abstract modular curves in positive characteristic2016

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

      Compositio Mathematica

      Volume: 152 Issue: 11 Pages: 2405-2442

    • DOI

      10.1112/s0010437x16007612

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Variation of fundamental groups of curves in positive characteristic2016

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

      Journal of Algebraic Geometry

      Volume: 26 Issue: 1 Pages: 1-16

    • DOI

      10.1090/jag/665

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] 共通同種因子を持つアーベル多様体の族について(Anna Cadoret氏との共同研究)2019

    • Author(s)
      玉川安騎男
    • Organizer
      大阪大学整数論保型形式セミナー
    • Related Report
      2019 Annual Research Report
  • [Presentation] Neukirch-内田の定理の長さm可解版について(Mohamed Saidi氏との共同研究)2019

    • Author(s)
      玉川安騎男
    • Organizer
      愛知数論セミナー
    • Related Report
      2019 Annual Research Report
  • [Presentation] 共通同種因子を持つアーベル多様体の族について(Anna Cadoret氏との共同研究)2019

    • Author(s)
      玉川安騎男
    • Organizer
      愛知数論セミナー
    • Related Report
      2019 Annual Research Report
  • [Presentation] アーベル多様体に関する3つの予想について2018

    • Author(s)
      玉川安騎男
    • Organizer
      香川セミナー(於香川大学)
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)2016

    • Author(s)
      Akio Tamagawa
    • Organizer
      東京北京パリ数論幾何セミナー(於東京大学)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 代数多様体の数論的基本群とその線形表現2016

    • Author(s)
      玉川安騎男
    • Organizer
      第61回代数学シンポジウム(於佐賀大学)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Fundamental groups and moduli of curves in positive characteristic2015

    • Author(s)
      Akio Tamagawa
    • Organizer
      Moduli Spaces and Arithmetic Geometry
    • Place of Presentation
      Lorentz Center
    • Year and Date
      2015-11-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Specialization of l-adic representations of arithmetic fundamental groups and applications to arithmetic of abelian varieties2015

    • Author(s)
      Akio Tamagawa
    • Organizer
      AMS Summer Institute in Algebraic Geometry
    • Place of Presentation
      University of Utah
    • Year and Date
      2015-07-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Remarks] 玉川 安騎男|京都大学数理解析研究所

    • URL

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

    • Related Report
      2019 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2018 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2017 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
      2016 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
      2015 Annual Research Report
  • [Funded Workshop] 副有限モノドロミー,ガロア表現,および複素関数2018

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] Inter-universal Teichmueller Theory Summit 20162016

    • Related Report
      2016 Annual Research Report

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Published: 2015-04-16   Modified: 2022-11-04  

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