We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

It is proved that for a commutative noetherian ring with dualizing complex the homotopy
category of projective modules is equivalent, as a triangulated category, to the homotopy …

Gorenstein derived categories are defined, and the relation with the usual derived
categories is given. The bounded Gorenstein derived categories of Gorenstein rings and of …

Gorenstein homological algebra is a kind of relative homological algebra which has been
developed to a high level since more than four decades. In this report we review the basic …

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves on a semi-
separated noetherian scheme, and study these complexes using the pure derived category …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …

We determine all the Gorenstein-projective modules over the T2-extension of a Gorenstein
algebra, and over (AM0B), where A and B are self-injective algebras, and M is an AB …

We study the category Rep (Q, M) of representations of a quiver Q with values in an abelian
category M. Under certain assumptions, we show that every cotorsion pair (A, B) in M …