On Matlis dualizing modules

On Matlis Dualizing Modules

We consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with respect to the other. Using this fact we argue that the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible (R,R)-bimodules. We show by example that...

An Auslander-buchsbaum Identity for Semi- Dualizing Modules

Semi-dualizing Modules and Related Gorenstein Homological Dimensions

A semi-dualizing module over a commutative noetherian ringA is a finitely generated module C with RHomA(C,C) ≃ A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call C–Gorenstein projective, C–Gorenstein injective, and C–Gorenstein flat dimension, and investigate the properties of these dimensions.

On the associated primes of Matlis duals of top local cohomology modules

After motivating the question we prove various results about the set of associated primes of Matlis duals of local cohomology modules. In easy cases we can calculate this set. An easy application of this theory is the well-known fact that Krull dimension can be expressed by the vanishing of local cohomology modules. 0. Motivation and Notation Whenever (R,m) is a noetherian local ring, we denote...

Rigid Dualizing Complexes on Schemes

In this paper we present a new approach to Grothendieck duality on schemes. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. We obtain most of the important features of Grothendieck duality, yet manage to avoid lengthy and difficult compatibility verifications. Our results apply to finite t...