… To prove our main result, Theorem 4.5, appearing in the next section we investigate further
the Gorenstein flat dimension and the cotorsion dimension of a complex. In particular, Lemma …

… We define the triangulated category of relative singularities of a closed … The appropriate
exotic derived category of coherent matrix … For any closed subscheme of finite flat dimension in a …

… We construct the relative singularity category with respect to Gorenstein (L,A)-flat modules,
as the … (L,A)-flat dimension and cotorsion dimension by the bounded homotopy category of …

… We study the properties of the relative derived category D C b ( A ) of an abelian category A
relative to … We introduce a dimension denoted by C D -dim M which is called the C -proper D -…

… singularity with a non-commutative resolution A = End R ( R ⊕ M ) . In this paper, we show
that the relative singularity category … for the complex ADE-singularities in all Krull dimensions. …

… flat dimension between schemes of finite Krull dimension, and the pushforwards of locally
free matrix factorizations of finite rank for any such morphism for which the induced morphism …

… dimensional algebras, this quotient category appeared in Rickard's work where he proved
that the singularity category … ring R, every flat module has finite projective dimension by [11, …

… dimensional affine Landau-Ginzburg model over S. Then every object in the dg category of
relative singularities … . As we are considering locally flat dg categories, it is immediate that this …

… We consider when the singularity category is triangle equivalent to the stable category of …
A regular (respectively, Gorenstein) category \(\mathcal {C}\) is called of dimension at most n if …

… finite projective dimension, then also the derived category of G … ], and so m has infinite pure
projective dimension in A = Flat-R. … We denote the class of relative I-cell complexes by I-cell. …