… is determined by the local singularity categories from … (relative) singularity categories in
singularity theory and representation theory. • Firstly, we study the relative singularity category …

… singularity with a non-commutative resolution A = End R ( R ⊕ M ) . In this paper, we show
that the relative singularity category … Moreover, it determines the classical singularity category …

… Then we introduce the relative singularity category T ω for a triangulated category T with
a … categories [28]. This generalizes the above-mentioned variants of singularity categories. …

… properties of the relative derived category D C b ( A ) of an abelian category A relative to a …
admissible and closed under direct summands, the C -singularity category D C - sg ( A ) = D C …

… relative singularity category with respect to a self-orthogonal subcategory ω of an abelian
category… More precisely, we study the relative singularity category equation image and various …

… We define the triangulated category of relative singularities of a closed … category of coherent
matrix factorizations is then identified with the triangulated category of relative singularities…

… category was first introduced by Buchweitz in [12] under the name of stabilized derived category
… the homological singularity of A, and we call it the singularity category of A after Orlov [34…

… as the Verdier quotient of the relative singularity category by the essential image of the above
functor, and we show an analogous result to that of F. Kong and P. Zhang [23, Theorem 6.8…

… More generally, we construct a relative singular coderived model M sing co ( A / R ) for any
morphism of dg rings φ : R → A as follows: first we show that the coderived model structure M …

… We introduce the concept of relative singularity category \(\… to a subcategory of the homotopy
category \(\mathbb {K} _\… description of the classical singularity category \(\mathbb {D} …