Reflexivity and rigidity for complexes, I: Commutative rings
type: Item
instance of: scholarly article
title: Reflexivity and rigidity for complexes, I: Commutative rings
zbMATH Open document ID: 1194.13017
author: Luchezar L. Avramov
author: Joseph Lipman
author: Srikanth B. Iyengar
published in: Algebra \& Number Theory
publication date: 2010-05-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/0904.4695
review text: Let \(R\) be a commutative noetherian ring and \(C\) a semidualizing complex for \(R\). In the present paper, the authors define \(C\)-rigid complexes and studied them. By using a suitable semidualizing complex, we can characterize rigid complexes in the sense of [\textit{M. Van den Bergh}, J. Algebra 195, No. 2, 662--679 (1997; Zbl 0894.16020); \textit{A. Yekutieli} and \textit{J. J. Zhang}, Trans. Am. Math. Soc. 360, No. 6, 3211--3248 (2008; Zbl 1165.18009), Algebr. Represent. Theory 12, No. 1, 19--52 (2009; Zbl 1186.14017)].
reviewed by: Takesi Kawasaki
Mathematics Subject Classification ID: 13D09
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 5704462
zbMATH Keywords: semidualizing complexes
zbMATH Keywords: perfect complexes
zbMATH Keywords: invertible complexes
zbMATH Keywords: rigid complexes
zbMATH Keywords: relative dualizing complexes
zbMATH Keywords: derived reflexivity
zbMATH Keywords: finite Gorenstein dimension
MaRDI profile type: Publication
OpenAlex ID: W2048107304
arXiv ID: 0904.4695
Wikidata QID: Q56003589
DOI: 10.2140/ANT.2010.4.47
description: scientific article