Lattices in rank one Lie groups over local fields

We prove that if {Mathematical expression} is the K-rational points of a K-rank one semisimple group {Mathematical expression} over a non archimedean local field K, then G has cocompact non-arithmetic lattices and if char(K)>0 also non-uniform ones. We also give a general structure theorem for lattices in G, from which we confirm Serre's conjecture that such arithmetic lattices do not satisfy the congruence subgroup property.