Cohomological dimension of complexes

الأصل · EN

In the derived category of the category of modules over a commutative Noetherian ring R, we define, for an ideal of R, two different types of cohomological dimensions of a complex X in a certain subcategory of the derived category, namely (, X)={(, ℓ(X))-ℓ|ℓ∈ Z} and -R(X), where (, M)={ℓ∈ Z|ℓ(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, - R(X)≤(, X) and equality holds if indeed (X) is finitely generated.