The main goal of this paper is to establish finiteness properties of local cohomology modules
in characteristic 0 that would be analogous to those proven by C. Huneke and R. Sharp in …

We continue the study of modules cofinite with respect to an ideal of a (noetherian
commutative) ring. Hartshorne [8] introduced this class of modules, answering in negative a …

Let $ A $ be a regular local ring of positive characteristic. This paper is concerned with the
local cohomology modules of $ A $ itself, but with respect to an arbitrary ideal of $ A $. The …

We show that if M is a finitely generated module over a commutative Noetherian local ring R
and I is a dimension one ideal of R (ie, dim RI= 1), then the local cohomology modules HIi …

Let R be a commutative Noetherian ring and let M be a non-zero finitely generated R-
module. Let I be an ideal of R and ta non-negative integer such that dimSuppHIi (M)⩽ 1 for …

COFINITENESS OF LOCAL COHOMOLOGY MODULES FOR IDEALS OF DIMENSION ONE
Page 1 K.-I. Yoshida Nagoya Math. J. Vol. 147 (1997), 179-191 COFINITENESS OF LOCAL …

Definition [4]. Let A be a noetherian ring,[afr] an ideal of A and M an A-module. M is said to
be [afr]-cofinite if M has support in V ([afr]) and ExtiA (A/[afr], M) is a finite A-module for each i …

Let R be ad-dimensional regular local ring, I an ideal of R, and M a finitely generated R-
module of dimension n. We prove that the set of associated primes of Ext Ri (R/I, H Ij (M)) is …

We study the Hodge filtration on the local cohomology sheaves of a smooth complex
algebraic variety along a closed subscheme Z in terms of log resolutions and derive …

Let A be a noetherian local ring, and I an ideal of A of dimension one. Our purpose of this
paper is to prove that the category M (A, I) _ cof of cofinite modules is Abelian …