Cofiniteness and finiteness of local cohomology modules over regular local rings

摘要

Let (R,m) be a commutative Noetherian regular local ring of dimension d and I be a proper ideal of R such that mAss (R) (R/I) = Assh (R) ((I)). It is shown that the R- module H-ht(I) (I) (R) is I-cofinite if and only if cd(I,R) = ht(I). Also we present a sufficient condition under which this condition the R-module H (i) (I) (R) is finitely generated if and only if it vanishes.