Wonderful compactifications of bruhat-tits buildings

Bertrand Rémy (1) , Amaury Thuillier (2) , Annette Werner (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 ICJ - Institut Camille Jordan
3 Institute for Mathematics [Frankfurt ]

Given a split semisimple group over a local field, we consider the maximal Satake-Berkovich compactification of the corresponding Euclidean building. We prove that it can be equivariantly identified with the compactification which we get by embedding the building in the Berkovich analytic space associated to the wonderful compactification of the group. The construction of this embedding map is achieved over a general non-archimedean complete ground field. The relationship between the structures at infinity, one coming from strata of the wonderful compactification and the other from Bruhat-Tits buildings, is also investigated.

Mots clés: algebraic group; wonderful compactification; non-archimedean local field; Bruhat-Tits building; Berkovich geometry

Domaines: Théorie des groupes [math.GR]; Géométrie algébrique [math.AG]

Bertrand Rémy, Amaury Thuillier, Annette Werner. Wonderful compactifications of bruhat-tits buildings. 2017. ⟨hal-01463953v1⟩