On top local cohomology modules, Matlis duality and tensor products

Abstract

Let a be an ideal of a local ring (R, m) with c = cd(a, R) the cohomological dimension of a in R. In the case that c = dim R, we first give a bound for depth D(H c a (R)), where c > 2 and (R, m) is complete. Later, H c a (R) ⊗ R H c a (R), D(H c a (R)) ⊗ R D(H c a (R)) and H c a (R) ⊗ R D(H c a (R)) are examined. In the case c = dim R − 1, the set Att R H c a (R) is considered.