The derived category analogue of some results in local cohomology
type: Item
instance of: scholarly article
title: The derived category analogue of some results in local cohomology
zbMATH Open document ID: 1390.13035
author: Bahman Jalali
author: Majid Rahro Zargar
author: Feysal Hassani
publication date: 2018-02-14T00:00:00Z
review text: In the paper under review, the authors provide the derived category analogue of some results about the local cohomology modules. The main result says that: Theorem. Let \(R\) be a commutative Noetherian ring with finite number of maximal ideals. Let \(Z\) be a subset of Spec\((R)\) that is stable under specialization. Then for any left bounded complex \(X\) of \(R\)-modules with finitely generated homology, the following equality holds: \(\mathrm{inf }\{i| H^i_Z (X)\) is not Artinian\(\}=\mathrm{inf }\{\mathrm{depth}_{R_p} X_p| p\in \mathrm{Z-Max }R\}\).
reviewed by: Siamak Yassemi
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13C60
Mathematics Subject Classification ID: 13D45
zbMATH DE Number: 6838833
zbMATH Keywords: derived category
zbMATH Keywords: local cohomology
zbMATH Keywords: cohomological dimension
MaRDI profile type: Publication
full work available at URL: s12215-016-0275-5
OpenAlex ID: W2529847865
cites work: Some results on local cohomology modules defined by a pair of ideals
cites work: Generalized Local Cohomology Modules and Homological Gorenstein Dimensions
cites work: Bounded complexes of flat modules
cites work: Q4451109
cites work: The derived category analogue of the Hartshorne-Lichtenbaum vanishing theorem
cites work: Depth for complexes, and intersection theorems
cites work: Local cohomology based on a nonclosed support defined by a pair of ideals
cites work: Q4049187
cites work: Generalized section functors
cites work: Abstract local cohomology functors
DOI: 10.1007/S12215-016-0275-5
published in: Rendiconti del Circolo Matematico di Palermo
Recommended article: The derived category analogues of Faltings Local-global Principle and Annihilator Theorems
Recommended article: Localization of triangulated categories and derived categories
Recommended article: Local cohomology in Grothendieck categories
Recommended article: The derived category analogue of the Hartshorne-Lichtenbaum vanishing theorem
Recommended article: Q4369240
Recommended article: Hochschild (co)homology and derived categories
Recommended article: On localizing subcategories of derived categories
Recommended article: Q4549264
Recommended article: Q5490915
Recommended article: Derived categories of coherent sheaves and equivalences between them
description: scientific article; zbMATH DE number 6838833