Wonderful compactifications of Bruhat-Tits buildings

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 asso...

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Bibliographic Details
Main Authors: Bertrand Remy, Amaury Thuillier, Annette Werner
Format: Article
Language:English
Published: Association Epiga 2017-12-01
Series:Épijournal de Géométrie Algébrique
Subjects:
Online Access:https://epiga.episciences.org/3133/pdf
Description
Summary: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.
ISSN:2491-6765