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2010 Reflexivity and rigidity for complexes, I: Commutative rings
Luchezar Avramov, Srikanth Iyengar, Joseph Lipman
Algebra Number Theory 4(1): 47-86 (2010). DOI: 10.2140/ant.2010.4.47

Abstract

A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main results characterizes C-rigid complexes. Specialized to the case when C is the relative dualizing complex of a homomorphism of rings of finite Gorenstein dimension, it leads to broad generalizations of theorems of Yekutieli and Zhang concerning rigid dualizing complexes, in the sense of Van den Bergh. Along the way, new results about derived reflexivity with respect to C are established. Noteworthy is the statement that derived C-reflexivity is a local property; it implies that a finite R-module M has finite G-dimension over R if Mm has finite G-dimension over Rm for each maximal ideal m of R.

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Luchezar Avramov. Srikanth Iyengar. Joseph Lipman. "Reflexivity and rigidity for complexes, I: Commutative rings." Algebra Number Theory 4 (1) 47 - 86, 2010. https://doi.org/10.2140/ant.2010.4.47

Information

Received: 15 April 2009; Revised: 15 July 2009; Accepted: 18 August 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1194.13017
MathSciNet: MR2592013
Digital Object Identifier: 10.2140/ant.2010.4.47

Subjects:
Primary: 13D05 , 13D25
Secondary: 13C15 , 13D03

Keywords: derived reflexivity , finite Gorenstein dimension , invertible complexes , perfect complexes , relative dualizing complexes , rigid complexes , semidualizing complexes

Rights: Copyright © 2010 Mathematical Sciences Publishers

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