An intrinsic characterization of Bruhat-Tits buildings inside analytic groups

Bertrand Rémy (1) , Annette Werner (2) , Amaury Thuillier (3, 4)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 Institut fur Mathematik Goethe Universität Frankfurt-am-Main
3 ICJ - Institut Camille Jordan
4 AGL - Algèbre, géométrie, logique

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.

Mots clés: algebraic group; valued field; Berkovich analytic geometry; Bruhat-Tits building AMS classification (2000): 20E42; 51E24; 14L15; 14G22

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

Bertrand Rémy, Annette Werner, Amaury Thuillier. An intrinsic characterization of Bruhat-Tits buildings inside analytic groups. The Michigan Mathematical Journal, 2022, 72, pp.543-557. ⟨10.1307/mmj/20217220⟩. ⟨hal-03343671⟩