Bruhat-Tits buildings and analytic geometry

TL;DR

This paper explores the theory of Bruhat-Tits buildings, their realization within Berkovich spaces, and how non-Archimedean analytic geometry provides a framework for their intrinsic description and compactification.

Contribution

It offers a comprehensive overview of Bruhat-Tits buildings and introduces their realization in Berkovich spaces, enhancing understanding through non-Archimedean analytic geometry.

Findings

Bruhat-Tits buildings can be embedded in Berkovich spaces

Berkovich geometry enables compactification of buildings

Intrinsic descriptions of buildings are achieved via non-Archimedean geometry

Abstract

This paper provides an overview of the theory of Bruhat-Tits buildings. Besides, we explain how Bruhat-Tits buildings can be realized inside Berkovich spaces. In this way, Berkovich analytic geometry canbe used to compactify buildings. We discuss in detail the example of the special linear group. Moreover, we give an intrinsic description of Bruhat-Tits buildings in the framework of non-Archimedean analytic geometry.