# Wonderful compactifications of Bruhat-Tits buildings

## TL;DR

This paper establishes a new equivariant identification between the Satake-Berkovich compactification of Euclidean buildings and the Berkovich analytic space of the wonderful compactification of a split semisimple group, over general non-archimedean fields.

## Contribution

It introduces a novel embedding of Euclidean buildings into Berkovich spaces, linking two compactification methods in a general non-archimedean setting.

## Key findings

- Equivariant identification of compactifications.
- Construction of embedding over non-archimedean fields.
- Analysis of structures at infinity from different compactifications.

## Abstract

Given a split semisimple group over a local field, we consider the maximal Satake-Berkovich compactification of the corresponding Euclidean building. We prove that it can be equivariantly identified with the compactification which we get by embedding the building in the Berkovich analytic space associated to the wonderful compactification of the group. The construction of this embedding map is achieved over a general non-archimedean complete ground field. The relationship between the structures at infinity, one coming from strata of the wonderful compactification and the other from Bruhat-Tits buildings, is also investigated.