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Maximality of hyperspecial compact subgroups avoiding Bruhat-Tits theory. (Maximalité des sous-groupes hyperspéciaux sans la théorie de Bruhat-Tits.) (English. French summary) Zbl 1483.20083

Summary: 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 \(\operatorname{GL}_n\) and avoids all considerations on the Bruhat-Tits building of \(G\).

MSC:

20G25 Linear algebraic groups over local fields and their integers
20E28 Maximal subgroups
20E42 Groups with a \(BN\)-pair; buildings
20G07 Structure theory for linear algebraic groups
14G20 Local ground fields in algebraic geometry
14L15 Group schemes
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