**Title:** *Products in the cohomology of local Hopf algebras *

**Abstract:** This is joint work with Lucho Avramov and Srikanth Iyengar. Suppose that A is a local commutative Hopf algebra over a field of prime characteristic. The question that we investigate is: How does the a change in the coalgebra structure alter the action of the cohomology ring on the cohomology of modules? This question is particularly interesting in the case that A is the group algebra in characteristic p of an abelian p-group. The algebra A can also be viewed as the restricted enveloping algebra of a commutative Lie algebra. But, the coalgebra structures that we would adopt in the tow settings are different. This leads to different actions on the cohomology of modules. We show that the action of a subring of the cohomology ring, that has the same Krull dimension, is independent of the choice of the coalgebra structure.