A comparison of adic spaces and Berkovich spaces

TL;DR

This paper explores the relationship between adic spaces and Berkovich spaces, establishing an explicit functorial equivalence between their categories for certain types of spaces.

Contribution

It provides an explicit construction of the equivalence using valuative spaces, clarifying the connection between these two frameworks in non-Archimedean geometry.

Findings

Establishes an explicit functorial equivalence between taut adic and Berkovich spaces.

Clarifies the role of valuative spaces in relating the two categories.

Provides a comprehensive review of the categorical relationship.

Abstract

This paper reviews the equivalence between the category of taut adic spaces that are locally of finite type and the category of strictly analytic Berkovich spaces. An explicit construction of this functor is provided by using the terminology of valuative spaces.