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Spring 2020 On the Gorenstein defect categories
Javad Asadollahi, Tahereh Dehghanpour, Rasool Hafezi
J. Commut. Algebra 12(1): 1-26 (Spring 2020). DOI: 10.1216/jca.2020.12.1

Abstract

The main theme of this paper is to study different “Gorenstein defect categories” and their connections. This is done by studying rings for which 𝕂 a c (  Prj- R ) = 𝕂 t a c (  Prj- R ) , that is, rings enjoying the property that every acyclic complex of projectives is totally acyclic. Such studies have been started by Iyengar and Krause over commutative Noetherian rings with a dualizing complex. We show that a virtually Gorenstein Artin algebra is Gorenstein if and only if it satisfies the above mentioned property. Then, we introduce recollements connecting several categories which help in providing categorical characterizations of Gorenstein rings. Finally, we study relative singularity categories that lead us to some more “Gorenstein defect categories”.

Citation

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Javad Asadollahi. Tahereh Dehghanpour. Rasool Hafezi. "On the Gorenstein defect categories." J. Commut. Algebra 12 (1) 1 - 26, Spring 2020. https://doi.org/10.1216/jca.2020.12.1

Information

Received: 20 July 2016; Revised: 25 May 2017; Accepted: 3 June 2017; Published: Spring 2020
First available in Project Euclid: 13 May 2020

zbMATH: 07211322
MathSciNet: MR4097053
Digital Object Identifier: 10.1216/jca.2020.12.1

Subjects:
Primary: 16E35, 16E65, 16G10, 16P10, 18E30

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 1 • Spring 2020
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