An intrinsic characterization of Bruhat-Tits buildings inside analytic groups

2021/09/13 by Bertrand Rémy, Rémy, Bertrand, Amaury Thuillier +3
Mathematics · #14G22 #14L15 #20E42 #51E24 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2109.05939

openalex publication_date 2021/09/13 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

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.

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