Singular equivalences of functor categories via Auslander-Buchweitz approximations

The aim of this paper is to construct singular equivalences between functor categories. As a special case, we show that there exists a singular equivalence arising from a cotilting module T, namely, the singularity category of (T-perpendicular to)/[T] and that of (mod Lambda)/ [T] are triangle equivalent. In particular, the canonical module w over a commutative Noetherian ring R induces a singular equivalence between (CMR)/[omega] and (mod R)/[omega], which generalizes Matsui-Takahashi's theorem. Our result is based on a sufficient condition for an additive category A and its subcategory X so that the canonical inclusion X -> A induces a singular equivalence D-sg (A) similar or equal to D-sg(X), which is a functor category version of Xiao-Wu Chen's theorem. (C) 2019 Elsevier Inc. All rights reserved.