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It is proved that the continuous bounded cohomology of SL2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for SL2 over S-integers.
Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban
Dimitri Stelio Wyss, Francesca Carocci, Giulio Orecchia