On Liu morphisms in non-Archimedean geometry

TL;DR

This paper introduces Liu morphisms in non-Archimedean geometry, establishing their properties and similarities to affine morphisms in scheme theory, thereby advancing the understanding of morphisms in Berkovich spaces.

Contribution

The paper defines Liu and quasi-Liu morphisms in Berkovich spaces and demonstrates their correspondence to affine and quasi-affine morphisms in scheme theory.

Findings

Liu morphisms behave like affine morphisms

Quasi-Liu morphisms behave like quasi-affine morphisms

Establishes a parallel between Berkovich and scheme morphisms

Abstract

We define Liu morphisms and quasi-Liu morphisms between Berkovich analytic spaces. We show that Liu morphisms and quasi-Liu morphisms behave exactly as affine morphisms and quasi-affine morphisms of schemes.