A STUDY OF COUSIN COMPLEXES THROUGH THE DUALIZING COMPLEXES

Dualizing Complexes

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 ...

DUALIZING COMPLEXES Contents

Duality for Cousin Complexes

We relate the variance theory for Cousin complexes − developed by Lipman, Nayak and the author to Grothendieck duality for Cousin complexes. Specifically for a Cousin complex F on (Y, ∆)—with ∆ a codimension function on a formal scheme Y (noetherian, universally catenary)—and a pseudo-finite type map f : (X, ∆) → (Y, ∆) of such pairs of schemes with codimension functions, we show there is a der...