… show that the local cohomology functor RΓ aassociated with a does not increase injective
dimension. Dually, the derived a-adic completion functor LΛ a does not increase at dimension. …

… dimÄ^ is the injective dimension of Jl in the category of Ä-modules and dimÄSupp^ is the
dimension of the support of *M in SpecÄ. In particular, if dimÄ Supp*^ = 0, then Jt is injective. In …

… , the projective, injective and flat dimensions of modules play an … injective and Gorenstein
flat dimensions are studied. … Since lim → commutes with the homology functor, we also get …

… cohomology modules, the notion of which was introduced by Herzog [16] in 1974. For two R
-modules M and N , the i th generalized local cohomology of … local cohomology modules, we …

… of local cohomology modules listed in 1.2.2. … injective dimension over the relevant rings are
very helpful) give a tiny foretaste of results about the vanishing of local cohomology modules …

… Let R be a two-dimensional normal graded ring over a field of … local cohomology module
H~+ (R) using the graded module … To consider the converse in dimension two we will prove the …

… dimensions and the injective dimensions for DG-modules introduced by Yekutieli. We explain
the details by focusing on the projective dimension and … H0 of the 0-th cohomology algebra …

… First we show that q'0 is injective. Let x C Ker '0. Since x C Ms, for any integer r > 0, we can …
ideal m, and dimension n. Then E is isomorphic to the local cohomology module Hrn(A) (see […

… M over a power series ring R = k [ x 1 , … , x n ] , the dimension of the top de Rham cohomology
module H D R n ( M ) is equal to the largest number of copies of the injective envelope E …

… over the enveloping algebra A', and must in general be infinite dimensional. To show that
Hn… the Harrison cohomology of an algebra with coefficients inan injective module vanishes. …