Relative Singularity Categories with Respect to Gorenstein Flat Modules

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

作者机构：Department of MathematicsNorthwest Normal University Department of MathematicsSoutheast University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2017年第33卷第11期

页      面：1463-1476页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主　　题：Triangle equivalence Gorenstein flat dimension cotorsion dimension stable category,derived category homotopy category 

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.