Gorenstein projective modules and recollements over triangular matrix rings

Let T=(RM0S) be a triangular matrix ring with R and S rings and RMS an R–S-bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result of Enochs, Cortés-Izurdiaga, and Torrecillas [Gorenstein conditions over triangular matrix rings, J. Pure Appl. Algebra 218 (2014), no. 8, 1544-1554]. Also, we consider when the recollement of Db(T‐Mod) restricts to a recollement of its subcategory Db(T‐Mod)fgp consisting of complexes with finite Gorenstein projective dimension. As applications, we obtain recollements of the stable category T‐GProj¯ and recollements of the Gorenstein defect category Ddef(T‐Mod).