Relative singularity categories II: DG models

Abstract

We study the relationship between singularity categories and relative singularity categories and discuss constructions of differential graded algebras of relative singularity categories. As consequences, we obtain structural results, which are known or generalise known results, on singularity categories of algebras with radical square zero, of non-commutative deformations of Kleinian singularities, of $S{L}_3(\mathbb{C})$-quotient singularities and of Gorenstein toric threefolds.

arXiv comment33 pages

References in corpus (8)

• Triangulated categories of singularities and D-branes in Landau-Ginzburg models
• Calabi-Yau algebras
• Relative singularity categories I: Auslander resolutions
• Frobenius categories, Gorenstein algebras and rational surface singularities
• On torsion torsionfree triples
• Derived categories of graded gentle one-cycle algebras
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Cited by in corpus (8)

• Singularity categories via the derived quotient
• The derived contraction algebra
• Singularity categories of deformations of Kleinian singularities
• A new equivalence between singularity categories of commutative algebras
• Noncommutative deformation theory, the derived quotient, and DG singularity categories
• The ST correspondence for proper non-positive dg algebras
• The lower extension groups and quotient categories
• Classifying dg-categories of matrix factorizations