Relative Singularity Categories with Respect to Gorenstein Flat Modules  

作　　者：Zhen Xing DI Zhong Kui LIU Xiao Xiang ZHANG 

机构地区：[1]Department of Mathematics,Northwest Normal University [2]Department of Mathematics,Southeast University

出　　处：《Acta Mathematica Sinica,English Series》2017年第11期1463-1476,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11601433 and 11261050);the Postdoctoral Science Foundation of China(Grant No.2106M602945XB);Northwest Normal University(Grant No.NWNU-LKQN-15-12)

摘　　要：Let R be a right coherent ring and D^b（R-Mod） the bounded derived category of left R-modules. Denote by D^b（R-Mod）[GF,C] the subcategory of D^b（R-Mod） consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K^b（F∩C） the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D^b（R-Mod）[GF,C]/K^b（F∩C,） is triangle-equivalent to the stable category GF∩C of the Frobenius category of all Gorenstein fiat and cotorsion left R-modules.Let R be a right coherent ring and D^b（R-Mod） the bounded derived category of left R-modules. Denote by D^b（R-Mod）[GF,C] the subcategory of D^b（R-Mod） consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K^b（F∩C） the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D^b（R-Mod）[GF,C]/K^b（F∩C,） is triangle-equivalent to the stable category GF∩C of the Frobenius category of all Gorenstein fiat and cotorsion left R-modules.

关 键 词：Triangle equivalence Gorenstein flat dimension cotorsion dimension stable category derived category homotopy category 

分 类 号：O153.3[理学—数学] O152.6[理学—基础数学]