Bertrand Remy ; Amaury Thuillier ; Annette Werner - Wonderful compactifications of Bruhat-Tits buildings

epiga:3133 - Épijournal de Géométrie Algébrique, December 12, 2017, Volume 1 - https://doi.org/10.46298/epiga.2017.volume1.3133
Wonderful compactifications of Bruhat-Tits buildingsArticle

Authors: Bertrand Remy 1; Amaury Thuillier 2; Annette Werner 3

  • 1 Centre de Mathématiques Laurent Schwartz
  • 2 Algèbre, géométrie, logique
  • 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.


Volume: Volume 1
Published on: December 12, 2017
Accepted on: December 1, 2017
Submitted on: February 10, 2017
Keywords: Mathematics - Group Theory,Mathematics - Algebraic Geometry
Funding:
    Source : OpenAIRE Graph
  • Méthodes géométriques en théorie de Lie; Funder: French National Research Agency (ANR); Code: ANR-15-CE40-0012

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