Ascent Properties of Auslander Categories
By L. Christensen, Henrik Holm. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2005
69 citations recorded by the source corpus.
Abstract Let $R$ be a homomorphic image of a Gorenstein local ring. Recent work has shown that there is a bridge between Auslander categories and modules of finite Gorenstein homological dimensions over $R$ . We use Gorenstein dimensions to prove new results about Auslander categories and vice versa. For example, we establish base change relations between the Auslander categories of the source and target rings of a homomorphism $\varphi :\,R\,\to \,S$ of finite flat dimension.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/507de9e69d90d6dfa2c87a3e8e3c5f818cf51461
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Citations in the corpus
- AB-Contexts and Stability for Gorenstein Flat Modules with Respect to Semidualizing Modules (2008, background): “.2)]. Conversely, assume that C is dualizing forR. Using Theorem I, it suffices to show that each R-module M has GFC-pdR(M) < ∞. Since C is dualizing, the trivial extension R⋉C is Gorenstein by [21, (7)]. Also, we have dim(R⋉C) = dim(R) < ∞ as Spec(R ⋉C) is in bijection with Spec(R). Thus, in th”