Non-Archimedean Big Picard Theorems

TL;DR

This paper establishes a non-Archimedean version of the Big Picard Theorem, demonstrating that certain holomorphic maps extend across punctures using Berkovich's non-Archimedean analytic spaces.

Contribution

It introduces a non-Archimedean analog of the classical theorem, applying Berkovich's theory to extend holomorphic maps in this setting.

Findings

Proves the non-Archimedean Big Picard Theorem

Uses Berkovich's theory of non-Archimedean analytic spaces

Extends holomorphic maps across punctures in non-Archimedean context

Abstract

A non-Archimedean analog of the classical Big Picard Theorem, which says that a holomorphic map from the punctured disc to a Riemann surface of hyperbolic type extends accross the puncture, is proven using Berkovich's theory of non-Archimedean analytic spaces.