  In this paper we provide a wildness criterion for any finite dimensional Hopf
algebra with finitely generated cohomology. This generalizes a result of
Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields
of arbitrary characteristic. Our proof uses the theory of support varieties for
modules, one of the crucial ingredients being a tensor product property for
some special modules. As an application we prove a conjecture of Cibils stating
that small quantum groups of rank at least two are wild.
