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hal-00366340, version 1

BRUHAT-TITS THEORY FROM BERKOVICH'S POINT OF VIEW.
I - REALIZATIONS AND COMPACTIFICATIONS OF BUILDINGS

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

(2009-03-06)

Abstract: We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group G over a suitable non-Archimedean field k we define a map from the Bruhat-Tits building B(G,k) to the Berkovich analytic space Gan asscociated with G. Composing this map with the projection of G^an to its flag varieties, we define a family of compactifications of B(G,k). This generalizes results by Berkovich in the case of split groups. Moreover, we show that the boundary strata of the compactified buildings are precisely the Bruhat-Tits buildings associated with a certain class of parabolics. We also investigate the stabilizers of boundary points and prove a mixed Bruhat decomposition theorem for them.

  • 1:  Institut Camille Jordan (ICJ)
  • CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon
  • 2:  Institut für Mathematik
  • Goethe-Universität Frankfurt
  • Domain : Mathematics/Algebraic Geometry
    Mathematics/Group Theory
  • Keywords : algebraic group – local field – Berkovich geometry – Bruhat-Tits building – compactification
 
  • hal-00366340, version 1
  • oai:hal.archives-ouvertes.fr:hal-00366340
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  • Submitted on: Friday, 6 March 2009 15:24:30
  • Updated on: Friday, 6 March 2009 17:28:06