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Given a locally finite leafless tree
, various algebraic groups over local fields might appear as closed subgroups of
. We show that the set of closed cocompact subgroups of
that are isomorphic to a quasi-split simple algebraic group is a closed subset of the Chabauty space of
. This is done via a study of the integral Bruhat–Tits model of
, that we carry on over arbitrary local fields, without any restriction on the (residue) characteristic. In particular, we show that in residue characteristic
, the Tits index of simple algebraic subgroups of
is not always preserved under Chabauty limits.