2003/05/08 by Mohammad T. Dibaei, Siamak Yassemi, Dibaei, Mohammad T. +1
Mathematics · #13D45 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #msc:13D45
paper · pdf · doi:10.48550/arxiv.math/0305119
13 pages
arxiv created 2003/05/08 · openalex publication_date 2003/05/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the derived category of the category of modules over a commutative Noetherian ring R, we define, for an ideal \fa of R, two different types of cohomological dimensions of a complex X in a certain subcategory of the derived category, namely \cd(\fa, X)=sup\\cd(\fa, \Hℓ(X))-ℓ|ℓ∈\Bbb Z\ and -inf\mathbf R\G\fa(X), where \cd(\fa, M)=sup\ℓ∈\Bbb Z|\Hℓ\fa(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, -inf \mathbf R\G\fa(X)≤\cd(\fa, X) and equality holds if indeed \H(X) is finitely generated.