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Paper   IPM / M / 2947
School of Mathematics
  Title:   Cohomological dimension of complexes
1.  M.T. Dibaei
2.  S. Yassemi
  Status:   Published
  Journal: Comm. Algebra
  Year:  2004
  Pages:   4375-4386
  Supported by:  IPM
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.

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