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Arithmetic and Moduli Spaces around Galois-Teichmueller tower

Research Project

Project/Area Number 21340009
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOsaka University (2013)
Okayama University (2009-2012)

Principal Investigator

NAKAMURA Hiroaki  大阪大学, 理学(系)研究科(研究院), 教授 (60217883)

Co-Investigator(Kenkyū-buntansha) TSUNOGAI Hiroshi  上智大学, 理工学部, 教授 (20267412)
ISHIKAWA Yoshihiro  岡山大学, 大学院・自然科学研究科, 助教 (50294400)
TAMAGAWA Akio  京都大学, 数理解析研究所, 教授 (00243105)
WATANABE Takao  大阪大学, 大学理学研究科, 教授 (30201198)
Co-Investigator(Renkei-kenkyūsha) MOCHIZUKI Shinichi  京都大学, 数理解析研究所, 教授 (10243106)
MATSUMOTO Makoto  広島大学, 大学院理学研究科, 教授 (70231602)
TOKUNAGA Hiroo  首都大学, 東京理工学研究科, 教授 (30211395)
FURUSHO Hidekazu  名古屋大学, 多元数理科学研究科, 准教授 (60377976)
HOSHI Yuichiro  京都大学, 数理解析研究所, 講師 (50456761)
TSUNOGAI Hiroshi  上智大学, 理工学部, 教授 (20267412)
ISHIKAWA Yoshihiro  岡山大学, 大学院・自然科学研究科, 助教 (50294400)
TAMAGAWA Akio  京都大学, 数理解析研究所, 教授 (00243105)
Project Period (FY) 2009-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥16,510,000 (Direct Cost: ¥12,700,000、Indirect Cost: ¥3,810,000)
Fiscal Year 2013: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2010: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2009: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Keywords数論幾何学 / モジュライ空間 / 基本群 / 遠アーベル幾何 / 代数学 / 国際研究者交流 / 整数論 / モノドロミー表現 / デデキント和 / 写像類群 / ガロア・タイヒミュラー理論 / 組みひも群 / Eisenstein級数
Research Abstract

In this project, researches on anabelian geometry have been developed with rich prospects for number theory and algebraic geometry. In particular, promoted were international interactions of arithmetic researches concerning Galois-Teichmueller tower formed by fundamental groups of algebraic curves and their moduli spaces. In October 2010, we realized the 3rd Seasonal Institute Conference of Mathematical Society of Japan in Kyoto University, and subsequently in October 2012 we published the proceedings volume "Galois-Teichmueller theory and Arithmetic Geometry". Besides, a certain monodromy invariant arising from fundamental groups of once-punctured elliptic curves was studied and research papers on it have been published.

Report

(6 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (33 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (17 results) (of which Peer Reviewed: 13 results) Presentation (14 results) (of which Invited: 10 results) Book (1 results) Remarks (1 results)

  • [Journal Article] On arithmetic monodromy representations of Eisenstein type in fundamental groups of once punctured elliptic curves2013

    • Author(s)
      H.Nakamura
    • Volume
      49
    • NAID

      110009623779

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On hyperbolic area of the moduli of θ-acute triangles2013

    • Author(s)
      N.Kanesaka, H.Nakamura
    • Volume
      55
    • Pages
      191-200
    • NAID

      120005197752

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On hyperbolic area of the moduli of theta-acute triangles2013

    • Author(s)
      N.Kanesaka, H.Nakamura
    • Journal Title

      Math. J. Okayama Univ.

      Volume: 55

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On arithmetic monodromy representations of Eisenstein type in fundamental groups of once punctured elliptic curves2013

    • Author(s)
      H.Nakamura
    • Journal Title

      Publ. RIMS, Kyoto University

      Volume: 49 Issue: 3 Pages: 413-496

    • DOI

      10.4171/prims/110

    • NAID

      110009623779

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some congruence properties of Eisenstein invariants associated to elliptic curves2012

    • Author(s)
      H.Nakamura
    • Journal Title

      Galois-Teichmueller theory and arithmetic geometry

      Volume: 63 Pages: 813-832

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Galois rigidity of fundamental groups of algebraic curves2012

    • Author(s)
      H.Nakamura
    • Journal Title

      Nonabelian Fundamental Groups and Iwasawa Theory

      Volume: 393 Pages: 56-71

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals2012

    • Author(s)
      H.Nakamura, Z.Wojtkowiak
    • Journal Title

      Nonabelian Fundamental Groups and Iwasawa Theory

      Volume: 393 Pages: 258-310

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals2012

    • Author(s)
      H.Nakamura
    • Journal Title

      London Math. Soc. Lecture Note Series

      Volume: 393

    • Related Report
      2012 Annual Research Report
  • [Journal Article] On Galois rigidity of fundamental groups of algebraic curves2012

    • Author(s)
      H.Nakamura
    • Journal Title

      London Math. Soc. Lecture Note Series

      Volume: 393

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Some congruence properties of Eisenstein invariants associated to elliptic curves2012

    • Author(s)
      H.Nakamura
    • Journal Title

      Advanced Studies in Pure Math

      Volume: 63

    • Related Report
      2012 Annual Research Report
  • [Journal Article] On Galois rigidity of fundamental groups of algebraic curves2012

    • Author(s)
      Hiroaki Nakamura
    • Journal Title

      London Math.Soc.Lecture Note Series

      Volume: 393 Pages: 56-71

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals2012

    • Author(s)
      Hiroaki Nakamura, Zdzislaw Wojtkowiak
    • Journal Title

      London Math.Soc.Lecture Note Series

      Volume: 393 Pages: 258-310

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Harmonic and equianharmonic equations in the Grothendieck- Teichmueller group, III2010

    • Author(s)
      H.Nakamura, H.Tsunogai, S.Yasuda
    • Journal Title

      Journal Inst. Math

      Volume: 9 Pages: 431-448

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Belyi function on X_0(49) of degree 72010

    • Author(s)
      K.Hoshino, H.Nakamura
    • Journal Title

      The Belyi functions and dessin d'enfants corresponding to the non-normal inclusions of triangle groups

      Volume: 52 Pages: 61-63

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Belyi function on X_0(49)of degree 72010

    • Author(s)
      Hiroaki Nakamura
    • Journal Title

      Mathematical Journal of Okayama University 52

      Pages: 61-63

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Harmonic and equianharmonic equations in the Grothendieck-Teichmueller group, III2010

    • Author(s)
      Hiroaki Nakamura
    • Journal Title

      Journal Inst. Math. Jussieu 9

      Pages: 431-448

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Galois analogue of functional equations of polylogarithms2009

    • Author(s)
      Hiroaki Nakamura
    • Journal Title

      Oberwolfach Reports 6

      Pages: 330-330

    • Related Report
      2009 Annual Research Report
  • [Presentation] On arithmetic Dehn-Nielsen mapping2013

    • Author(s)
      H. Nakamura
    • Organizer
      Number Theory Seminar
    • Place of Presentation
      University of Nottingham
    • Year and Date
      2013-03-20
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Some observation in Johnson homomorphisms2013

    • Author(s)
      H.Nakamura
    • Organizer
      Workshop "Johnson homomorphisms"
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2013 Annual Research Report
  • [Presentation] Ascending a tower of Galois-Teichmueller in higher genera2012

    • Author(s)
      H.Nakamura
    • Organizer
      Seminaire "Arithmetique et Topologie" a Lille
    • Place of Presentation
      Laboratoire Paul Painleve , Universite Lille 1
    • Year and Date
      2012-11-29
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On some arithmetic monodromy invariant for once punctured torus, Workshop2012

    • Author(s)
      H.Nakamura
    • Organizer
      Masanori Morishita
    • Place of Presentation
      Kyushu University, Fukuoka
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] An introduction to moduli spaces related to elliptic curves2011

    • Author(s)
      H.Nakamura
    • Organizer
      Heilbronn Institute for Mathematical Research
    • Place of Presentation
      Univ. of Bristol
    • Year and Date
      2011-05-02
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] An introduction to moduli spaces related to elliptic curves2011

    • Author(s)
      中村博昭
    • Organizer
      Heilbronn Day : Background Workshop on Multiple Zeta Values, Modular Forms & Elliptic Motives
    • Place of Presentation
      Heilbronn Institute for Mathematical Research, University of Bristol(招待講演)
    • Year and Date
      2011-05-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] Arithmetic invariants related to Eisenstein series arising from metaabelian monodromy representations of once punctured elliptic curves", Workshop on Multiple Zeta Values, Modular Forms and Elliptic Motives, (organized by Herbert Gangl, Richard Hain, Owen Patashnick)2011

    • Author(s)
      H.Nakamura
    • Organizer
      Heilbronn Institute for Mathematical Research
    • Place of Presentation
      Univ. of Bristol
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] カルダノ・フェラーリと楕円関数論再訪2010

    • Author(s)
      中村博昭
    • Organizer
      数学系代数分野談話会
    • Place of Presentation
      筑波大学
    • Year and Date
      2010-06-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] On fundamental groups of once punctured elliptic curves2010

    • Author(s)
      H.Nakamura
    • Organizer
      Seminar "Theorie de Galois et methodes explicites" at Laboratoire Paul Painleve
    • Place of Presentation
      Lille University
    • Year and Date
      2010-03-23
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On an elliptic analgue of Ihara's power series2010

    • Author(s)
      H.Nakamura
    • Organizer
      Workshop "Geometric and differential Galois theory"
    • Place of Presentation
      C.I.R.M., Luminy
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Galois analogue of functional equations of polylogarithms2009

    • Author(s)
      H.Nakamura
    • Organizer
      Workshop "The Arithmetic of Fields"
    • Place of Presentation
      Oberwolfach, Germany
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Computing functional equations of l-adic polylogarithms on Galois group2009

    • Author(s)
      H.Nakamura
    • Organizer
      Workshop "Anabelian Geometry"
    • Place of Presentation
      Issac Newton Institute for Mathematical Sciences, Cambridge UK
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Arithmetic invariants of Eisenstein type arising from fundamental groups of once punctured elliptic curves2009

    • Author(s)
      H.Nakamura
    • Organizer
      "Final workshop" of Programme " Non-Abelian Fundamental Groups in Arithmetic Geometry"
    • Place of Presentation
      Isaac Newton Institute for Mathematical Sciences
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Arithmetic invariants of Eisenstein type arising from fundamental groups of once punctured elliptic curves2009

    • Author(s)
      Hiroaki Nakamura
    • Organizer
      "Final workshop" of Programme "Non-Abelian Fundamental Groups in Arithmetic Geometry"
    • Place of Presentation
      Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
    • Related Report
      2009 Annual Research Report
  • [Book] Galois-Teichmüller theory and Arithmetic Geometry2012

    • Author(s)
      H.Nakamura, F.Pop, L.Schneps, A.Tamagawa
    • Publisher
      Mathematical Society of Japan
    • Related Report
      2013 Final Research Report
  • [Remarks]

    • URL

      http://www.math.sci.osaka-u.ac.jp/~nakamura/index.html

    • Related Report
      2013 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

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