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| Paper IPM / M / 2947 |
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| Abstract: | |||||
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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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