… pure-global dimension of rings. Moreover, invariance of pure … It is also worth noting that a
proof of the flat cover conjecture … derived category, the following shows that the relative derived …

… 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 …

… singularity R, we show that the relative singularity category Δ … R ) , together with the Krull
dimension, is enough to recover R… exceptional locus recovers the singularity category. As a first …

… dimension), D s g b ( A ) measures how far A is from the smoothness. For some work on the
… GP ( A ) is a Frobenius category with relative projective–injective objects being projective …

… 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. …

… is of finite projective dimension. (2) Singularity categories may be described as relative … :
(1) for a Gorenstein ring R, every flat module has finite projective dimension by [11], Chapter 9, …

… the singularity category and the stable module category of a selfinjective algebra, due to
Rickard [40, Theorem 2.1]. The notion of singular equivalence of finite dimensional algebras …

… setting, we characterize rings of finite finitistic dimension. … of flat-cotorsion sheaves on X,
the singularity category takes … in Section 2 two singularity categories relative to the projective …

… , using the equivalence with the singularity category and the notion of … with relatively proper
support. To check that these two … Gorenstein of Krull dimension n, the injective dimension of A …

… dg categories to be homotopically flat; if not we need to first … some preliminaries on relative
singularity categories, which we … that Πλ(Q) has finite global dimension, so we need to find a …