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  Chabauty limits of algebraic groups acting on trees: the quasi-split case

Stulemeijer, T. (2020). Chabauty limits of algebraic groups acting on trees: the quasi-split case. Journal of the Institute of Mathematics of Jussieu, 19(4), 1031-1091. doi:10.1017/S1474748018000282.

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Stulemeijer_Chabauty limits of algebraic groups acting on trees the quasi-split case_2020.pdf (Publisher version), 972KB
 
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https://doi.org/10.1017/S1474748018000282 (Publisher version)
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Stulemeijer, Thierry1, Author              
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: 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) haracteristic. 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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Language(s): eng - English
 Dates: 2020
 Publication Status: Published in print
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 Rev. Type: Peer
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Title: Journal of the Institute of Mathematics of Jussieu
  Abbreviation : J. Inst. Math. Jussieu
Source Genre: Journal
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Publ. Info: Cambridge University Press
Pages: - Volume / Issue: 19 (4) Sequence Number: - Start / End Page: 1031 - 1091 Identifier: -