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  • Thierry Stulemeijer (a1)

Given a locally finite leafless tree $T$ , various algebraic groups over local fields might appear as closed subgroups of $\operatorname{Aut}(T)$ . We show that the set of closed cocompact subgroups of $\operatorname{Aut}(T)$ that are isomorphic to a quasi-split simple algebraic group is a closed subset of the Chabauty space of $\operatorname{Aut}(T)$ . This is done via a study of the integral Bruhat–Tits model of $\operatorname{SL}_{2}$ and $\operatorname{SU}_{3}^{L/K}$ , that we carry on over arbitrary local fields, without any restriction on the (residue) characteristic. In particular, we show that in residue characteristic $2$ , the Tits index of simple algebraic subgroups of $\operatorname{Aut}(T)$ is not always preserved under Chabauty limits.

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Postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn.

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Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
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