… subcategory of an abelian category. In this paper we investigate the singularity category \(\…
)\) of the stable category \(\underline{\mathcal {X}}\) of \(\mathcal {X}\). We consider when the …

… of the bounded derived category of Noetherian objects of A by the subcategory of compact
… summands equivalent to the subcategory of compact objects in the homotopy category K ac ( …

… The singularity category of X is the triangulated quotient category Dsg(X) := Db(Coh(X))/
Perf(X), where Perf(X) denotes the full subcategory of complexes which are locally quasi-…

… paper is to introduce Gorenstein singularity category D g p s … derived category D g p b ( A )
by the triangulated subcategory … abelian category, then the Gorenstein singularity category D …

… category is independent of the chosen normalization. Based on this, we define the singularity
and cosingularity categories … be concerned with a number of other subcategories of D ( R ) …

… So we want to consider the difference between the triangulated category Db(mod-A) and
its triangulated subcategory per(A). In other words, we are interested in the (Verdier) quotient …

… subcategories of the stable derived category of any affine scheme that has hypersurface
singularities or … , this classifies the thick subcategories of the singularity categories of such rings. …

… For an exact category \({{\mathcal {E}}}\) with enough … tilting subcategory, we show that the
singularity category of \({{\mathcal {E}}}\) admits a \(d\mathbb {Z}\)-cluster tilting subcategory. …

… The singularity category of an algebra is defined to be the Verdier quotient of the bounded
derived category with respect to the thick subcategory formed by complexes isomorphic to …

… The singularity category of an algebra is defined to be the … derived category with respect to
the thick subcategory formed … , the singularity category measures the homological singularity …