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IPM
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“School of Mathematics”

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Paper   IPM / M / 15523
School of Mathematics
  Title:   Stable under specialization sets and cofiniteness
  Author(s):  Kamran Divaani-Aazar (Joint with H. Faridian and M. Tousi)
  Status:   Published
  Journal: J. Algebra Appl.
  Year:  2019
  Pages:   DOI: 10.1142/S0219498819500154
  Supported by:  IPM
  Abstract:
Let R be a commutative noetherian ring, and Z a stable under specialization subset of \Spec(R). We introduce a notion of Z-cofiniteness and study its main properties. In the case dim(Z) ≤ 1, or dim(R) ≤ 2, or R is semilocal with \cd(Z,R) ≤ 1, we show that the category of Z-cofinite R-modules is abelian. Also, in each of these cases, we prove that the local cohomology module HiZ(X) is Z-cofinite for every homologically left-bounded R-complex X whose homology modules are finitely generated and every i ∈ \mathbbZ.

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