We prove, under the assumption of the virtual fibration conjecture for arithmetic
hyperbolic 3-manifolds, that all arithmetic lattices in O(n,1), n> 4, and different from
7, are non-coherent. We also establish noncoherence of uniform arithmetic lattices of the
simplest type in SU(n,1), n> 1, and of uniform lattices in SU(2,1) which have infinite
abelianization.