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Symonds' proof of Benson's regularity conjecture implies that the regularityof the cohomology of a fusion system and that of the Hochschild cohomology of ap-block of a finite group is at most zero. Using results of Benson, Greenlees,and Symonds, we show that in both cases the regularity is equal to zero.

On the Castelnuovo-Mumford regularity of the cohomology of fusion systems and of the Hochschild cohomology of block algebras