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An asymptotic behavior of solutions of p-adic differential equations

Research Project

Project/Area Number 15H06261
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

Ohkubo Shun  名古屋大学, 多元数理科学研究科, 助教 (20755160)

Project Period (FY) 2015-08-28 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsp進微分方程式 / Gauss-Manin接続
Outline of Final Research Achievements

We studied Chiarellotto-Tsuzuki's conjecture on the growth of solutions of p-adic differential equations with Frobenius structures over open unit ball. Our basic approach is based on the author's previous work (2017, Adv. Math.) using certain cyclic vectors with respect to Frobenius structures. In the article written by T. Nakagawa(2013、Tohoku), we found a certain condition on the determination of the growth. We considered a related condition to Nakagawa's condition, and for rank~3 differential equation satisfies this condition, we could verify Chiarellotto-Tsuzuki's conjecture.

Report

(3 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Annual Research Report
  • Research Products

    (3 results)

All 2017 2016

All Presentation (3 results) (of which Invited: 3 results)

  • [Presentation] On the rationality of the logarithmic growth filtration of solutions of p-adic differential equations2017

    • Author(s)
      Shun Ohkubo
    • Organizer
      Seminaire de Geometrie Arithmetique
    • Place of Presentation
      Universite de Rennes (France)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] On the rationality of the logarithmic growth filtration of solutions of p-adic differential equations2017

    • Author(s)
      Shun Ohkubo
    • Organizer
      Geometrie analytique et equations differentielles p-adiques
    • Place of Presentation
      CIRM (France)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] On the rationality of the logarithmic growth filtration of solutions of p-adic differential equations2016

    • Author(s)
      Shun Ohkubo
    • Organizer
      Seminaire Theorie des Nombres
    • Place of Presentation
      Universite Bordeaux (France)
    • Related Report
      2016 Annual Research Report
    • Invited

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Published: 2015-08-26   Modified: 2018-03-22  

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