- The motivation for the work presented in this paper was two questions posed by M. Artin. Let A be a d dimensional regular graded algebra over the field k, with augmentation ideal m (see Def. 4.13). Denote by Hi(A) (resp. Hi,(A)) the dth left (resp. right) local cohomology of A at the ideal m; i.e., Hi(A) = lim,, Extd,(A/m”, A) and similarly for Hi,(A). As left modules and as right modules, Hi(A) and H$,(A) are both isomorphic to A’ := Hom,(A, k) (up to a twist in degrees; all operations are taking place in the graded category).