Descent for non-archimedean analytic spaces

TL;DR

This paper investigates descent properties in Berkovich analytic spaces, focusing on flat descent and descent via field extensions, revealing that the most significant results concern descent with respect to field extensions.

Contribution

It provides new insights into descent phenomena in non-archimedean analytic geometry, especially highlighting the importance of descent with respect to ground field extensions.

Findings

Descent of properties like being a good analytic space.

Descent of morphisms without boundary.

Field extension descent plays a crucial role.

Abstract

In this paper we study two types of descent in the category of Berkovich analytic spaces: flat descent and descent with respect to an extension of the ground field. Quite surprisingly, the deepest results in this direction seem to be of the second type, including the descent of properties of being a good analytic space and being a morphism without boundary.