Pierre-Emmanuel Caprace: Characterising rank one groups

Pierre-Emmanuel Caprace, Université Catholique de Louvain

Abstract: We present necessary and sufficient conditions for a locally compact group acting properly on a locally finite tree to be isomorphic to SL2 over a local field k of arbitrary characteristic. This can be used to provide a characterisation of SL2(k) among locally compact groups, in the spirit of Hilbert's fifth problem. More general rank one groups will also be considered.