Applications of balanced pairs  

作　　者：LI HuanHuan WANG JunFu HUANG ZhaoYong 

机构地区：[1]Department of Mathematics, Nanjing University

出　　处：《Science China Mathematics》2016年第5期861-874,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11171142)

摘　　要：Let(X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to(X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y(resp. Y-coresolution dimension of X)is finite, then the bounded homotopy category of Y(resp. X) is contained in that of X(resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite.Let（X, Y） be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to（X, Y）, and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y（resp. Y-coresolution dimension of X）is finite, then the bounded homotopy category of Y（resp. X） is contained in that of X（resp. Y）. As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite.

关 键 词：balanced pairs relative cotorsion pairs relative derived categories relative singularity categories relative（co）resolution dimension 

分 类 号：O154.1[理学—数学]