Bruhat–Tits theory from Berkovich’s point of view. Analytic filtrations

Abstract

We define filtrations by affinoid groups, in the Berkovich analytification of a connected reductive group, related to Moy–Prasad filtrations. They are parametrized by a cone, whose basis is the Bruhat–Tits building and whose vertex is the neutral element, via the notions of Shilov boundary and holomorphically convex envelope.