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Investigation of degenerations and uniformizations by means of rigid geometry

Research Project

Project/Area Number 26400050
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionTokyo Institute of Technology (2015-2016)
Kumamoto University (2014)

Principal Investigator

Kato Fumiharu  東京工業大学, 理学院, 教授 (50294880)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsリジッド幾何学 / 代数幾何学 / トロピカル幾何学 / Berkovich幾何学
Outline of Final Research Achievements

(1) A totally new p-adic uniformization with torsion in dimension two, which gives rise to a fake projective plane which is, however, non-isomorphic to the Mumford's one, has been observed for the first time, in the course of our enduring investigation for higher dimensional non-archimedean "orbifold uniformization", viz., uniformization with torsion elements.
(2) The full-scale theorization of the so-called "Henselian rigid geometry" has been embarked, probably for the first time in this field of mathematical researches, as a new conceptualization of most modern algebro-geometric and rigid-analytic hybrid spaces, which will, expectedly, enhance the arithmetico- and algebro-geometric aspects of the classical rigid geometry.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (10 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (2 results) Journal Article (3 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 3 results,  Open Access: 1 results) Presentation (5 results) (of which Int'l Joint Research: 3 results,  Invited: 4 results)

  • [Int'l Joint Research] Utrecht University(オランダ)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Padova University(イタリア)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] A fake projective plane via 2-adic uniformization with torsion2017

    • Author(s)
      Daniel Allcock and Fumiharu Kato
    • Journal Title

      Tohoku Math. J.

      Volume: 69

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Buchberger stratification on the space of polynomials2015

    • Author(s)
      Fumiharu Kato, Kei Ohnoshi
    • Journal Title

      Kumamoto J. Math.

      Volume: 28 Pages: 1-10

    • NAID

      110009930182

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A combinatorial Li-Tau inequality and rational points on curves2015

    • Author(s)
      Gunther Cornelissen, Fumiharu Kato, Janne Kool
    • Journal Title

      Math. Ann.

      Volume: 361 Issue: 1-2 Pages: 211-258

    • DOI

      10.1007/s00208-014-1067-x

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] On Henselian rigid geometry2016

    • Author(s)
      Fumiharu Kato
    • Organizer
      Conference “Algebraic Geometry in East Asia 2016”
    • Place of Presentation
      University of Tokyo
    • Year and Date
      2016-01-19
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Zariski Main Theorem for henselian rigid spaces2015

    • Author(s)
      Fumiharu Kato
    • Organizer
      Conference “Non-archimedean analytic geometry: Theory and Practice”
    • Place of Presentation
      Maison de la Culture, Papeete, Tahiti
    • Year and Date
      2015-08-25
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Non-archimedean geometry ― past and present2015

    • Author(s)
      Fumiharu Kato
    • Organizer
      A Symposium on the History of Functional Analysis
    • Place of Presentation
      School of Mathematics, Northwest University, Xian, China
    • Year and Date
      2015-05-09
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] From Tate curves to Zariski-Riemann spaces --- A guide to a birational approach to rigid geometry2014

    • Author(s)
      Fumiharu Kato
    • Organizer
      Higher Invariants
    • Place of Presentation
      Regensburg University (Germany)
    • Year and Date
      2014-08-28 – 2014-09-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Fake projective planes2014

    • Author(s)
      Fumiharu Kato
    • Organizer
      The 4th South Kyushu workshop on algebra
    • Place of Presentation
      熊本大学くすの木会館
    • Year and Date
      2014-07-22 – 2014-07-25
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2018-03-22  

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