Singular equivalences of functor categories via Auslander-Buchweitz approximations

Abstract

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⊥)/[T] and that of (modΛ)/[T] are triangle equivalent. In particular, the canonical module ω over a commutative Noetherian ring R induces a singular equivalence between (CMR)/[ω] and (modR)/[ω], 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 Dsg(A)≃Dsg(X), which is a functor category version of Xiao-Wu Chen's theorem.