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Further developments of inter-universal Teichmuller theory

Research Project

Project/Area Number 15K04781
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionKyoto University

Principal Investigator

Yamashita Go  京都大学, 数理解析研究所, 講師 (70444453)

Co-Investigator(Kenkyū-buntansha) 望月 新一  京都大学, 数理解析研究所, 教授 (10243106)
Project Period (FY) 2015-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords宇宙際Teichmuller理論 / 遠アーベル幾何 / Hodge-Arakelov理論 / ゼータ関数 / L関数 / Siegel零点 / 宇宙際幾何 / Riemannゼータ
Outline of Final Research Achievements

The co-investigator Mochizuki showed that we can generalise inter-universal Teichmuller theory for
elliptic curves with complex multiplications. Hence, he obtained a relationship between inter-universal Teichmuller theory and the zeros of Dirichlet L-functions. This can be regarded as the first step of studies of the zeros of zeta functions via further developments of inter-universal geometry.

Academic Significance and Societal Importance of the Research Achievements

ゼータ関数の零点の研究は極めて困難であるが、宇宙際Teichmuller理論によるabc予想の証明においてはいわゆる「一元体上の微分」に相当する現象が起こっているため、宇宙際幾何学の手法によるアプローチは有力であると思われる。今回、宇宙際Teichmuller理論とDirichlet L関数の零点の間に関係が生まれたことはゼータ関数の零点の研究にとって大きな第一歩である。ゼータ関数の零点に関するRiemann予想はクレイによって挙げられている21世紀に解決すべき7つの問題の1つであり、まだRiemann予想までの道のりは遠いが最初の第一歩を踏み出せたことは社会的意義も大きいと感じる。

Report

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

    (17 results)

All 2018 2017 2016 2015 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (8 results) (of which Int'l Joint Research: 6 results,  Invited: 7 results) Remarks (2 results) Funded Workshop (1 results)

  • [Journal Article] A small remark on finite multiple zeta values and $p$-adic multiple zeta values.2017

    • Author(s)
      Go Yamashita
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B68 Pages: 171-174

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A small remark on the filtered $\phi$-module of Fermat varieties and Stickelberger's theorem2016

    • Author(s)
      Go Yamashita
    • Journal Title

      Tsukuba J. Math.

      Volume: 40 Issue: 1 Pages: 119-124

    • DOI

      10.21099/tkbjm/1474747490

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Bogomolov’s proof of the geometric version of the Szpiro Conjecture from the point of view of inter-universal Teichm¨uller theory2016

    • Author(s)
      Shinichi Mochizuki
    • Journal Title

      Res. Math. Sci.

      Volume: 3 Issue: 1

    • DOI

      10.1186/s40687-016-0057-x

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Bogomolov’s Proof of the Geometric Version of the Szpiro Conjecture from the Point of View of Inter-universal Teichm¨uller Theory2016

    • Author(s)
      Shinichi Mochizuki
    • Journal Title

      Res. Math. Sci.

      Volume: 3

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Topics in Absolute Anabelian Geometry III: Global Reconstruction Algorithms2015

    • Author(s)
      Shinichi Mochizuki
    • Journal Title

      J. Math. Sci. Univ. Tokyo

      Volume: 22 Pages: 939-1156

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Monomorphisms in Categories of Log Schemes2015

    • Author(s)
      Shinichi Mochizuki
    • Journal Title

      Kodai Math. J.

      Volume: 38 Pages: 365-429

    • NAID

      130005475916

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] A Proof of the ABC Conjecture after Mochizuki2018

    • Author(s)
      Go Yamashita
    • Organizer
      Pan Asia Number Theory Conference 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Reductions of crystalline representations and Hypergeometric polynomials2018

    • Author(s)
      Go Yamashita
    • Organizer
      Pan Asia Number Theory Conference 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A Proof of the ABC Conjecture after Mochizuk2018

    • Author(s)
      Go Yamashita
    • Organizer
      seminaire de theorie des nombres at Institut de Mathematiques de Jussieu
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] ABC Conjecture and Inter-universal Teichmuller Theory2018

    • Author(s)
      Go Yamashita
    • Organizer
      集中講義於慶應義塾大学
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] The mathematics of mutually alien copies: from Gaussian integrals to inter-universal Teichm¨uller theory2016

    • Author(s)
      Shinichi Mochizuki
    • Organizer
      Inter-universal Teichmuller Theory Summit 2016
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-07-19
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] IUTchIII-IV with remarks on the function-theoretic roots of the theory2016

    • Author(s)
      Go Yamashita
    • Organizer
      Inter-universal Teichmuller Theory Summit 2016
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] IUT-III2015

    • Author(s)
      Go Yamashita
    • Organizer
      Clay Math. Institute Workshop: IUT Theory of Shinichi Mochizuki
    • Place of Presentation
      Oxford大学
    • Year and Date
      2015-12-11
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] IUT-III and IUT-IV section 1 with some remarks on the language of species2015

    • Author(s)
      Go Yamashita
    • Organizer
      Clay Math. Institute Workshop: IUT Theory of Shinichi Mochizuki
    • Place of Presentation
      Oxford大学
    • Year and Date
      2015-12-11
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] Go Yamashita Official Homepage

    • URL

      http://www.kurims.kyoto-u.ac.jp/~gokun/

    • Related Report
      2018 Research-status Report 2017 Research-status Report 2016 Research-status Report 2015 Research-status Report
  • [Remarks] 望月新一@数理研

    • URL

      http://www.kurims.kyoto-u.ac.jp/~motizuki/top-japanese.html

    • Related Report
      2018 Research-status Report 2017 Research-status Report 2016 Research-status Report 2015 Research-status Report
  • [Funded Workshop] Inter-universal Teichmuller Theory Summit 20162016

    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-07-18
    • Related Report
      2016 Research-status Report

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Published: 2015-04-16   Modified: 2021-02-19  

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