Les squelettes accessibles d'un espace de Berkovich

TL;DR

This paper introduces a new class of skeletons called 'accessible' on Berkovich analytic spaces, demonstrating their stability under various morphisms and including standard torus skeletons.

Contribution

It defines the accessible skeletons on Berkovich spaces and proves their invariance under G-glueing, inverse images, and proper direct images.

Findings

Accessible skeletons include standard torus skeletons.

Accessible skeletons are preserved under G-glueing.

They are stable under inverse images and proper direct images.

Abstract

We define a class of skeletons on Berkovich analytic spaces, which we call "accessible", which contains the standard skeleton of the n-dimensional torus for every n and is preserved by G-glueing, by taking the inverse image along a morphism of relative dimension zero, and by taking the direct image along a morphism whose restriction to the involved skeleton is topologically proper.