Semi-dualizing complexes and their Auslander categories

An Auslander-buchsbaum Identity for Semi- Dualizing Modules

Dualizing Complexes

Symmetric Auslander and Bass Categories

We define the symmetric Auslander category A(R) to consist of complexes of projective modules whose leftand righttails are equal to the leftand right-tails of totally acyclic complexes of projective modules. The symmetric Auslander category contains A(R), the ordinary Auslander category. It is well known that A(R) is intimately related to Gorenstein projective modules, and our main result is th...

RIGID DUALIZING COMPLEXES

Let $X$ be a sufficiently nice scheme. We survey some recent progress on dualizing complexes. It turns out that a complex in $kinj X$ is dualizing if and only if tensor product with it induces an equivalence of categories from Murfet's new category $kmpr X$ to the category $kinj X$. In these terms, it becomes interesting to wonder how to glue such equivalences.

Recognizing Dualizing Complexes

Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. This paper proves that M is a dualizing complex for A if and only if the trivial extension A ⋉M is a Gorenstein Differential Graded Algebra. As a corollary follows that A has a dualizing complex if and only if it is a quotient of a Gorenstein local Differential Graded Algebra. Let A be a noetherian local ...