Recollements associated to cotorsion pairs over upper triangular matrix rings

Abstract

Let A, B be two rings and T = A M 0 B with M an A-B-bimodule. Given two complete hereditary cotorsion pairs (A A , B A ) and (C B , D B ) in A-Mod and B-Mod respectively. We define two cotorsion pairs (Φ(A A , C B ), Rep(B A , D B )) and (Rep(A A , C B ), Ψ(B A , D B )) in T -Mod and show that both of these cotorsion pairs are complete and hereditary. Given two cofibrantly generated model structures M A and M B on A-Mod and B-Mod respectively. Using the result above, we investigate when there exist a cofibrantly generated model structure M T on T -Mod and a recollement of Ho(M T ) relative to Ho(M A ) and Ho(M B ). Finally, some applications are given in Gorenstein homological algebra.