  We use the theory of varieties for modules arising from Hochschild cohomology
to give an alternative version of the wildness criterion of Bergh and Solberg:
If a finite dimensional self-injective algebra has a module of complexity at
least 3 and satisfies some finiteness assumptions on Hochschild cohomology,
then the algebra is wild. We show directly how this is related to the analogous
theory for Hopf algebras that we developed. We give applications to many
different types of algebras: Hecke algebras, reduced universal enveloping
algebras, small half-quantum groups, and Nichols (quantum symmetric) algebras.
