Singular equivalence and singular locus

For a commutative Gorenstein Noetherian ring R, we construct an affine scheme X solely from singularity category Dₒ₆ (R) of R such that there is a finite surjective morphism X Spec (R /I), where Spec (R /I) is the singular locus in Spec (R). As an application, for two such rings with equivalent singularity categories, we prove that the singular loci in their affine schemes have the same dimension.