English

Hyperbolicity notions for varieties defined over a non-Archimedean field

Algebraic Geometry 2018-01-09 v1

Abstract

Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semi distance dCK that he introduced for analytic spaces defined over a non-Archimedean metrized field k. We prove various characterizations of smooth projective varieties for which dCK is an actual distance. Secondly, we explore several notions of hyperbolicity for a smooth algebraic curve X defined over k. We prove a non-Archimedean analogue of the equivalence between having negative Euler characteristic and the normality of certain families of analytic maps taking values in X.

Keywords

Cite

@article{arxiv.1801.02479,
  title  = {Hyperbolicity notions for varieties defined over a non-Archimedean field},
  author = {Rita Rodríguez Vázquez},
  journal= {arXiv preprint arXiv:1801.02479},
  year   = {2018}
}
R2 v1 2026-06-22T23:39:20.215Z