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Bruhat-Tits theory from Berkovich’s point of view. I. Realizations and compactifications of buildings

Bertrand Rémy, Amaury Thuillier, Annette Werner (2010)

Annales scientifiques de l'École Normale Supérieure

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 ( G , k ) to the Berkovich analytic space G an associated with G . Composing this map with the projection of G an to its flag varieties, we define a family of compactifications of ( G , k ) . This generalizes results by Berkovich in the case of split groups. Moreover,...

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