Compactification of the Bruhat-Tits building of PGL by seminorms

Abstract

We construct a compactification of the Bruhat-Tits building associated to the group PGL(V) which can be identified with the space of homothety classes of seminorms on V endowed with the topology of pointwise convergence. Then we define a continuous map from the projective space to this compactification which extends the reduction map from Drinfeld's p-adic symmetric domain to the building.