An intrinsic characterization of Bruhat-Tits buildings inside analytic groups

TL;DR

This paper provides an intrinsic geometric characterization of how Bruhat-Tits buildings embed into analytic groups over non-Archimedean fields, enhancing understanding of their structure and compactifications.

Contribution

It introduces a new intrinsic description of the embedding of Bruhat-Tits buildings into analytic groups, clarifying their geometric and algebraic properties.

Findings

Intrinsic characterization of the embedding established

Enhanced understanding of building compactifications

Connections between algebraic groups and analytic geometry clarified

Abstract

Given a semisimple group over a complete non-Archimedean field, it is well known that techniques from non-Archimedean analytic geometry provide an embedding of the corresponding Bruhat-Tits builidng into the analytic space associated to the group; by composing the embedding with maps to suitable analytic proper spaces, this eventually leads to various compactifications of the building. In the present paper, we give an intrinsic characterization of this embedding.