… Viewing Λk as a Z/kZ-graded algebra naturally and considering the singularity category
Dsg(modZ/kZ(Λk)), we prove that the above triangulated equivalence induces a triangulated …

… behavior of singularity categories and stable categories of Gorenstein projective modules
along a morphism of rings. The natural context to approach the problem is via change of rings, …

… in local rings. Moreover, we find out several classes of local rings containing or contained
in the class of dominant … A local ring |$R$| is said to have an isolated singularity if it is …

… define an h-extension of a local ring R to be a separable extension RA of local rings such that
A is the localization at … Recall that a local ring R, m has an isolated singularity provided R is …

… This forces us to think first about how to define a “large” singularity category for R (admitting …
for this large singularity category. Given a locally Noetherian Grothendieck category A with …

… complete local ring with a perfect residue field, then the annihilator of the singularity category
… We establish a relationship between the annihilator of the singularity category of R and the …

… One also obtains a characterization of Gorenstein local rings R in terms of modules over the
stable category \({\mathsf {\underline{mod\,}}}R\), whose artinian case is none other than [55, …

… We will recall relevant background in Section 3, but readers wishing to think concretely may
consider an ordinary local ring with residue field k or R = C ⁎ ( B G ) ⟶ k . Numerous other …

… In Section 3, after stating some basics from commutative algebra, we explore complexities
for the singularity category of a singular local ring, and prove our main results including the …

… is to classify the rings which are the complete local rings at … ” singularities, for this caso each
complete local ring can be identified with a complete subring of the formal power series ring …