Tilting complexes and Auslander-Reiten conjecture.
type: Item
instance of: scholarly article
title: Tilting complexes and Auslander-Reiten conjecture.
zbMATH Open document ID: 1291.16006
author: Jiaqun Wei
published in: Mathematische Zeitschrift
publication date: 2012-10-22T00:00:00Z
review text: An open problem in the theory of finitely presented modules over Artin algebras is the Auslander-Reiten conjecture which states that if \(X\) is a finitely presented module over an Artin algebra \(R\) such that \(\mathrm{Ext}^i_R(X,X\oplus R)=0\) for all \(i>0\) then \(X\) is projective. In the present paper the author proves that this conjecture is stable under derived equivalences (Theorem 4.4). In order to do this Wei develops an interesting study of self-orthogonal objects in the bounded derived category associated to a coherent ring (Section 3).
reviewed by: Simion Sorin Breaz
Mathematics Subject Classification ID: 16E35
Mathematics Subject Classification ID: 16E05
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16G10
zbMATH DE Number: 6097128
zbMATH Keywords: Auslander-Reiten conjecture
zbMATH Keywords: tilting complexes
zbMATH Keywords: derived equivalences
zbMATH Keywords: bounded derived categories
zbMATH Keywords: finitely presented modules
zbMATH Keywords: Artin algebras
MaRDI profile type: Publication
full work available at URL: s00209-011-0941-4
OpenAlex ID: W1978471878
Wikidata QID: Q123114424
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DOI: 10.1007/S00209-011-0941-4
description: scientific article; zbMATH DE number 6097128