Altered local uniformization of Berkovich spaces

TL;DR

This paper proves that any compact quasi-smooth strictly $k$-analytic space can be covered by a space with a strictly semistable formal model after a finite extension and quasi-étale cover, extending Hartl's theorem to non-discrete valuations.

Contribution

It extends Hartl's local uniformization theorem to the case of non-discrete valuation fields for compact quasi-smooth strictly $k$-analytic spaces.

Findings

Existence of finite extension and quasi-étale cover for uniformization

Extension of Hartl's theorem to non-discrete valuation fields

Construction of strictly semistable formal models

Abstract

We prove that for any compact quasi-smooth strictly $k$-analytic space $X$ there exist a finite extension $l/k$ and a quasi-\'etale covering $X'\to X\otimes_kl$ such that $X'$ possesses a strictly semistable formal model. This extends a theorem of U. Hartl to the case of the ground field with a non-discrete valuation.