Algebra/Topology Seminar

Speaker: Corina-Gabriela Ciobotaru

Title: Chabauty limits of various subgroups of SL(n,Q_p)

Abstract: For a locally compact group G the set of all its closed subgroups S(G) is endowed with the Chabauty topology, under which S(G) becomes a compact space. Given a family of closed subgroups of G it is then natural to try to explicitly compute its closure in S(G) and see if the properties of the family are preserved for the limit subgroups.

In a recent joint project with Arielle Leitner, and separately in a joint article with Arielle Leitner and Alain Valette, we study Chabauty limits of various closed subgroups of SL(n, Q_p). Those groups include the diagonal Cartan subgroup of SL(n,Q_p), maximal compact subgroups of SL(n,Q_p), and the subgroups of all fixed points of involutions of SL(n,Q_p). All those subgroups stabilise specific subsets of the Bruhat—Tits building of SL(n,Q_p) and have a precise geometrical meaning. In particular, our results on Chabauty limits will produce limits of p-adic geometries and aim for a good understanding of the geometric transition between those geometries.