Torus embeddings and dualizing complexes

Torus embeddings and algebraic intersection complexes

In [GM2], Goreskey and MacPherson defined and constructed intersection complexes for topological pseudomanifolds. The complexes are defined in the derived category of sheaves of modules over a constant ring sheaf. Since analytic spaces are of this category, any algebraic variety defined over C has an intersection complex for each perversity. The purpose of this paper is to give an algebraic des...

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