Lehto-Virtanen-type and big Picard-type theorems for Berkovich analytic spaces (Algebraic Number Theory and Related Topics 2018)

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Abstract

In non-archimedean setting, we establish a Lehto–Virtanen-type theorem for a morphism from the punctured Berkovich closed unit disk D {0} in the Berkovich affine line to the Berkovich projective line P1 having an isolated essential singularity at the origin, and then establish a big Picard-type theorem for such an open subset Ω in the Berkovich projective space P^[N] of any dimension N that the family of all morphisms from D {0} to Ω is normal in a non-archimedean Montel’s sense. As an application of the latter theorem, we see a big Brody-type hyperbolicity of the Berkovich harmonic Fatou set of an endomorphism of P^[N] of degree > 1.

Algebraic Number Theory and Related Topics 2018. November 26-30, 2018. edited by Takao Yamazaki and Shuji Yamamoto. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

Journal

  • RIMS Kokyuroku Bessatsu

    RIMS Kokyuroku Bessatsu B86 279-286, 2021-07

    Research Institute for Mathematical Sciences, Kyoto University

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Details 詳細情報について

  • CRID
    1050007902932839040
  • NII Article ID
    120007145007
  • NII Book ID
    AA12196120
  • HANDLE
    2433/265160
  • ISSN
    18816193
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB
    • CiNii Articles

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