Eventually homological isomorphisms and Gorenstein projective modules  

作　　者：Yongyun Qin Dawei Shen 

机构地区：[1]School of Mathematics,Yunnan Normal University,Kunming 650500,China [2]School of Mathematics and Statistics,Henan University,Kaifeng 475004,China

出　　处：《Science China Mathematics》2024年第8期1719-1734,共16页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12061060 and 11801141);Scientific and Technological Planning Project of Yunnan Province(Grant No.202305AC160005);Scientific and Technological Innovation Team of Yunnan Province(Grant No.2020CXTD25)。

摘　　要：We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.

关 键 词：singularity categories Gorenstein defect categories Gorenstein projective modules AuslanderReiten conjecture Gorenstein symmetry conjecture eventually homological isomorphisms 

分 类 号：O154.1[理学—数学]