Maximality of hyperspecial compact subgroups avoiding Bruhat-Tits theory

2015/09/08 by Marco Maculan, Maculan, Marco
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1509.02449

To appear at "Annales de l'Institut Fourier". This version avoids completely Berkovich geometry

arxiv created 2016/05/16 · arxiv updated 2016/05/17

Abstract

Let k be a complete non-archimedean field (non trivially valued). Given a reductive k-group G, we prove that hyperspecial subgroups of G(k) (i.e. those arising from reductive models of G) are maximal among bounded subgroups. The originality resides in the argument: it is inspired by the case of \textrmGL_n and avoids all considerations on the Bruhat-Tits building of G.

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