Arithmetic and Moduli Spaces around Galois-Teichmueller tower

• Project/Area Number: 21340009
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka 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: ¥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.

Research Products

• [Journal Article] On arithmetic monodromy representations of Eisenstein type in fundamental groups of once punctured elliptic curves (2013)
  • Author(s): H.Nakamura
  • Volume: 49
  • NAID: 110009623779
  • Peer Reviewed
• [Journal Article] On hyperbolic area of the moduli of θ-acute triangles (2013)
  • Author(s): N.Kanesaka, H.Nakamura
  • Volume: 55
  • Pages: 191-200
  • NAID: 120005197752
  • Peer Reviewed
• [Journal Article] On hyperbolic area of the moduli of theta-acute triangles (2013)
  • Author(s): N.Kanesaka, H.Nakamura
  • Journal Title: Math. J. Okayama Univ. Volume: 55
  • Peer Reviewed
• [Journal Article] On arithmetic monodromy representations of Eisenstein type in fundamental groups of once punctured elliptic curves (2013)
  • Author(s): H.Nakamura
  • Journal Title: Publ. RIMS, Kyoto University Volume: 49 Issue: 3 Pages: 413-496
  • DOI: 10.4171/prims/110
  • NAID: 110009623779
  • Peer Reviewed
• [Journal Article] Some congruence properties of Eisenstein invariants associated to elliptic curves (2012)
  • Author(s): H.Nakamura
  • Journal Title: Galois-Teichmueller theory and arithmetic geometry Volume: 63 Pages: 813-832
  • Peer Reviewed
• [Journal Article] On Galois rigidity of fundamental groups of algebraic curves (2012)
  • Author(s): H.Nakamura
  • Journal Title: Nonabelian Fundamental Groups and Iwasawa Theory Volume: 393 Pages: 56-71
  • Peer Reviewed
• [Journal Article] Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals (2012)
  • Author(s): H.Nakamura, Z.Wojtkowiak
  • Journal Title: Nonabelian Fundamental Groups and Iwasawa Theory Volume: 393 Pages: 258-310
  • Peer Reviewed
• [Journal Article] Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals (2012)
  • Author(s): H.Nakamura
  • Journal Title: London Math. Soc. Lecture Note Series Volume: 393
• [Journal Article] On Galois rigidity of fundamental groups of algebraic curves (2012)
  • Author(s): H.Nakamura
  • Journal Title: London Math. Soc. Lecture Note Series Volume: 393
• [Journal Article] Some congruence properties of Eisenstein invariants associated to elliptic curves (2012)
  • Author(s): H.Nakamura
  • Journal Title: Advanced Studies in Pure Math Volume: 63
• [Journal Article] On Galois rigidity of fundamental groups of algebraic curves (2012)
  • Author(s): Hiroaki Nakamura
  • Journal Title: London Math.Soc.Lecture Note Series Volume: 393 Pages: 56-71
  • Peer Reviewed
• [Journal Article] Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals (2012)
  • Author(s): Hiroaki Nakamura, Zdzislaw Wojtkowiak
  • Journal Title: London Math.Soc.Lecture Note Series Volume: 393 Pages: 258-310
  • Peer Reviewed
• [Journal Article] Harmonic and equianharmonic equations in the Grothendieck- Teichmueller group, III (2010)
  • Author(s): H.Nakamura, H.Tsunogai, S.Yasuda
  • Journal Title: Journal Inst. Math Volume: 9 Pages: 431-448
  • Peer Reviewed
• [Journal Article] Belyi function on X_0(49) of degree 7 (2010)
  • 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
  • Peer Reviewed
• [Journal Article] Belyi function on X_0(49)of degree 7 (2010)
  • Author(s): Hiroaki Nakamura
  • Journal Title: Mathematical Journal of Okayama University 52 Pages: 61-63
  • Peer Reviewed
• [Journal Article] Harmonic and equianharmonic equations in the Grothendieck-Teichmueller group, III (2010)
  • Author(s): Hiroaki Nakamura
  • Journal Title: Journal Inst. Math. Jussieu 9 Pages: 431-448
  • Peer Reviewed
• [Journal Article] Galois analogue of functional equations of polylogarithms (2009)
  • Author(s): Hiroaki Nakamura
  • Journal Title: Oberwolfach Reports 6 Pages: 330-330
• [Presentation] On arithmetic Dehn-Nielsen mapping (2013)
  • Author(s): H. Nakamura
  • Organizer: Number Theory Seminar
  • Place of Presentation: University of Nottingham
  • Year and Date: 2013-03-20
  • Invited
• [Presentation] Some observation in Johnson homomorphisms (2013)
  • 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
• [Presentation] Ascending a tower of Galois-Teichmueller in higher genera (2012)
  • 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
  • Invited
• [Presentation] On some arithmetic monodromy invariant for once punctured torus, Workshop (2012)
  • Author(s): H.Nakamura
  • Organizer: Masanori Morishita
  • Place of Presentation: Kyushu University, Fukuoka
  • Invited
• [Presentation] An introduction to moduli spaces related to elliptic curves (2011)
  • Author(s): H.Nakamura
  • Organizer: Heilbronn Institute for Mathematical Research
  • Place of Presentation: Univ. of Bristol
  • Year and Date: 2011-05-02
  • Invited
• [Presentation] An introduction to moduli spaces related to elliptic curves (2011)
  • 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
• [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
  • 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
• [Presentation] On fundamental groups of once punctured elliptic curves (2010)
  • 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
  • Invited
• [Presentation] On an elliptic analgue of Ihara's power series (2010)
  • Author(s): H.Nakamura
  • Organizer: Workshop "Geometric and differential Galois theory"
  • Place of Presentation: C.I.R.M., Luminy
  • Invited
• [Presentation] Galois analogue of functional equations of polylogarithms (2009)
  • Author(s): H.Nakamura
  • Organizer: Workshop "The Arithmetic of Fields"
  • Place of Presentation: Oberwolfach, Germany
  • Invited
• [Presentation] Computing functional equations of l-adic polylogarithms on Galois group (2009)
  • Author(s): H.Nakamura
  • Organizer: Workshop "Anabelian Geometry"
  • Place of Presentation: Issac Newton Institute for Mathematical Sciences, Cambridge UK
  • Invited
• [Presentation] Arithmetic invariants of Eisenstein type arising from fundamental groups of once punctured elliptic curves (2009)
  • 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
  • Invited
• [Presentation] Arithmetic invariants of Eisenstein type arising from fundamental groups of once punctured elliptic curves (2009)
  • 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.
• [Book] Galois-Teichmüller theory and Arithmetic Geometry (2012)
  • Author(s): H.Nakamura, F.Pop, L.Schneps, A.Tamagawa
  • Publisher: Mathematical Society of Japan
• [Remarks]
  • URL: http://www.math.sci.osaka-u.ac.jp/~nakamura/index.html