## “School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 2947
School of Mathematics
Title:   Cohomological dimension of complexes
Author(s):
 1 M.T. Dibaei 2 S. Yassemi
Status:   Published
Journal: Comm. Algebra
Year:  2004
Pages:   4375-4386
Supported by:  IPM
Abstract:
In the derived category of the category of modules over a commutative Noetherian ring R, we define, for an ideal \fraka of R, two different types of cohomological dimensions of a complex X in a certain subcategory of the derived category, namely cd(\fraka, X)=sup{cd(\fraka,Hl(X))−l|l ∈ \mathbb Z} and −infRΓ\fraka(X), where cd(\fraka,M)=sup{l ∈ \mathbb Z|Hl\fraka(M) ≠ 0} for an R-module M. In this paper, it is shown, among other things, that, for any complex X bounded to the left, −infRΓ\fraka(X) ≤ cd(\fraka, X) and equality holds if indeed H(X) is finitely generated.