Bruhat-Tits buildings and analytic 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.

Survey written for the proceedings of the summer school "Berkovich spaces" held in Paris in July 2010. Revised version of October 2014: section 5 removed for futher elaboration. To appear in "Berkovich Spaces and Applications", Lecture Notes in Mathematics, Springer