Singularity categories with respect to Ding projective modules (Q2403994)

A module \(M\) is called Ding projective if we can find an exact sequence \(\cdots\to P^{-1}\to P^{0}\overset{\alpha} {P^1} \cdots \) which stays exact under the functors \(\mathrm{Hom}(-,F)\) for all flat modules \(F\) such that \(M\) is the kernel of \(\alpha\). In the present paper the authors study the singularity category constructed with respect to Ding modules over a ring \(R\), i.e. the Verdier quotient \(\mathbf{D}^b_{\mathcal{DP}}(R)/\mathbf{K}^b(\mathcal{DP})\) of the bounded derived category \(\mathbf{D}^b_{\mathcal{DP}}(R)\) constructed as the quotient category of homotopy category of \(R\) modulo those complexes which are are acyclic with respect to Ding projective modules, and with denominators in the bounded homotopy category associated to Ding projective modules.