# Duflot-type theorem for Hopf algebras ?

In group cohomology Duflot's theorem states that the depth of the mod p cohomology ring of a finite group is greater than or equal to the p-rank of the center of a Sylow p-subgroup.

Is there a corresponding result for the cohomology of a finite dimensional cocommutative Hopf algebra (or, equivalently, a finite group scheme) ?

Any hint is appreciated.

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It might be helpful to refer explicitly to Jeanne Duflot's basic paper for background. Aside from that, is there a natural analogue of the p-rank of the center of a Sylow p-subgroup? –  Jim Humphreys Sep 7 '10 at 15:21