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Chabauty limits of diagonal Cartan subgroups of SL(n,Qp)

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  • Corina-Gabriela Ciobotaru
  • Arielle Leitner, Weizmann Institute of Science, Israel
  • Alain Valette, University of Neuchatel, Switzerland

Let C be the subgroup of all diagonal matrices in SL(n,Q p). In the first part of this paper we study and give a classification of the Chabauty limits of SL(n,Q p)-conjugates of C using the action of SL(n,Q p) on its associated Bruhat–Tits building. Along the way we construct an explicit homeomorphism between the Chabauty compactification in sl(n,Q p) of SL(n,Q p)-conjugates of the p-adic Lie algebra of C and the Chabauty compactification of SL(n,Q p)-conjugates of C. In the second part of the paper we compute all of the Chabauty limits for n≤4 (up to conjugacy). In contrast, for n≥7 we prove there are infinitely many SL(n,Q p)-nonconjugate Chabauty limits.

Original languageEnglish
JournalJournal of Algebra
Pages (from-to)69-104
Number of pages36
Publication statusPublished - Apr 2022

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