Let R be a commutative Noetherian ring, let I be an ideal of R, and let M, N be two finitely
generated R-modules. The aim of this paper is to investigate the I-cofiniteness of …

Bounds for the Castelnuovo-Mumford regularity of Ext modules, over a polynomial ring over
a field, are given in terms of the initial degrees, Castelnuovo-Mumford regularities and the …

We investigate the asymptotic behavior of Castelnuovo-Mumford regularity of Ext and Tor,
with respect to the homological degree, over complete intersection rings. We derive from a …

Abstract Set A:= Q/(z), where Q is a polynomial ring over a field, and z= z 1,…, zc is a
homogeneous Q-regular sequence. Let M and N be finitely generated graded A-modules …

Let R be a commutative Noetherian ring and M, N be two finitely generated R-modules. In
this note, we prove the cofiniteness of generalized local cohomology modules H^ i _ I (M, N) …

Let R=⊕ n∈ ℕ 0 R n R=⊕_n∈N_0R_n be a Noetherian homogeneous ring with irrelevant
ideal R+=⊕ n∈ ℕ R n R_+=⊕_n∈NR_n and with local base ring (R 0, m 0) (R_0,m_0). Let …

We prove a duality theorem for graded algebras over a field that implies several known
duality results: graded local duality, versions of Serre duality for local cohomology and of …

BOUNDING COHOMOLOGY OF PROJECTIVE SCHEMES Page 1 BOUNDING
COHOMOLOGY OF PROJECTIVE SCHEMES CIMPA-TUBITAK SUMMER SCHOOL …

Let R be a standard graded algebra over a field k. We prove an Auslander–Buchsbaum
formula for the absolute Castelnuovo–Mumford regularity, extending important cases of …

Let R=⊕ j≥ 0Rj be a positively graded Noetherian ring with local base ring (R0, m0) and
the irrelevant ideal R+=⊕ j≥ 1Rj. Let M, N be two finitely generated graded R-modules with …