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Development of arithmetic topology and arithmetic quantum field theory

Research Project

Project/Area Number 24340005
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Algebra
Research InstitutionKyushu University

Principal Investigator

Morishita Masanori  九州大学, 数理(科)学研究科(研究院), 教授 (40242515)

Research Collaborator Terashima yuji  
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2013: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Keywords結び目 / 素数 / 3次元多様体 / 代数体 / 数論的位相幾何学 / 結び目と素数 / 素粒子 / 場の理論
Outline of Final Research Achievements

Based on the analogies between knots and primes, I studied arithmetic topology.
・We introduced the notion for S, which is a finite set S of primes of a number field containing a primitive m-th root of unity, to be link type. Then we introduce the multiple power residue symbols for such an S which generalize the power residue symbols and the Redei triple symbols. In particuler, we constructed the triple symbols over the cubic cyclotomic field. I wrote the joint paper with Fumiya Amano on this work (submitted). ・Following the analogies with Selmer module and the associated algebraic p-adic L-function for deformations of a Galois representation, we introduced the Selmer module and the associated L-function for deformations of a SL(2)-representation of a knot group, and gave an affirmative answer to Mazur's problem for some concrete examples. I wrote
the joint paper with Takahiro Kitayama, Ryoto Tange, Yuji Terashima on this work (submitted).

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (16 results)

All 2016 2014 2013 2012 Other

All Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 3 results,  Open Access: 1 results) Presentation (9 results) (of which Invited: 5 results) Remarks (1 results) Funded Workshop (1 results)

  • [Journal Article] Arithmetic Milnor invariants and multiple power residue symbols in number fields - a precis2016

    • Author(s)
      Fumiya Amano, Masanori Morishita
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] 平方剰余と結び目2016

    • Author(s)
      森下昌紀
    • Journal Title

      数学セミナー

      Volume: 55 Pages: 22-27

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Redei's triple symbols and modular forms2013

    • Author(s)
      F. Amano, H. Kodani, M. Morishita, T. Sakamoto, T. Yoshida, T. Ogasawara
    • Journal Title

      Tokyo J. Math.

      Volume: 36 Pages: 405-427

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nilpotent class field theory for manifolds2013

    • Author(s)
      J. Kim, H. Kotani, M. Morishita
    • Journal Title

      Proc. Japan Academy

      Volume: 89 Pages: 15-19

    • NAID

      40019605933

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Johnson maps in non-Abelian Iwasawa theory2012

    • Author(s)
      M. Morishita
    • Journal Title

      Oberwolfach Report

    • Related Report
      2012 Annual Research Report
  • [Presentation] Arithmetic Milnor invariants and multiple power residue symbols2014

    • Author(s)
      Masanori Morishita
    • Organizer
      Algebraic number theory and related topics
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-12-02
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Johnson maps in non-Abelian Iwasawa theory2013

    • Author(s)
      M. Morishita
    • Organizer
      整数論研究集会
    • Place of Presentation
      早稲田大学理工学部(招待講演)
    • Year and Date
      2013-03-17
    • Related Report
      2012 Annual Research Report
  • [Presentation] Johnson maps in non-Abelian Iwasawa theory2013

    • Author(s)
      M. Morishita
    • Organizer
      Conference on number theory and related topics in honor of Takashi Ono
    • Place of Presentation
      Johns Hopkins University, USA
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Milnor invariants for primes and Maass wave forms2013

    • Author(s)
      M. Morishita
    • Organizer
      Quantum Topology and Hyperbolic Geometry
    • Place of Presentation
      Nha Trang, Vietnam
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 結び目理論と整数論 -- 数論的位相幾何学2013

    • Author(s)
      森下昌紀
    • Organizer
      ENCOUNTERwithMATHEMATICS
    • Place of Presentation
      中央大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Johnson-Kawazumi maps in non-Abelian Iwasawa theory I, II2013

    • Author(s)
      M. Morishita
    • Organizer
      Workshop: Johnson homomorphisms
    • Place of Presentation
      東京大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Redei記号とMass波動形式2012

    • Author(s)
      森下昌紀
    • Organizer
      北陸数論研究集会
    • Place of Presentation
      金沢サテライトプラザ(招待講演)
    • Year and Date
      2012-12-26
    • Related Report
      2012 Annual Research Report
  • [Presentation] On Johnson maps in non-Abelian Iwasawa theory2012

    • Author(s)
      M. Morishita
    • Organizer
      Low dimensional topology and number theory
    • Place of Presentation
      Oberwolfach, Germany(招待講演)
    • Year and Date
      2012-08-30
    • Related Report
      2012 Annual Research Report
  • [Presentation] Knots and Primes - An Introduction to Anthmetic Topology2012

    • Author(s)
      M. Morishita
    • Organizer
      Japan-Taiwan conference on number theory
    • Place of Presentation
      National center for theoretical science, Taiwan(招待講演)
    • Related Report
      2012 Annual Research Report
  • [Remarks] Low dimensional topology and number theory

    • URL

      http://www2.math.kyushu-u.ac.jp/~morisita/workshop.html

    • Related Report
      2013 Annual Research Report
  • [Funded Workshop] Low dimensional topology and number theory VIII2016

    • Place of Presentation
      福岡
    • Year and Date
      2016-03-22
    • Related Report
      2015 Annual Research Report

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Published: 2012-04-24   Modified: 2019-07-29  

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