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# Ascent Properties of Auslander Categories

Published:2009-02-01
Printed: Feb 2009
• Lars Winther Christensen
• Henrik Holm
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## 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 $\varphi \colon R \to S$ of finite flat dimension.
 Keywords: Auslander categories, Gorenstein dimensions, ascent properties, Auslander--Buchsbaum formulas
 MSC Classifications: 13D05 - Homological dimension 13D07 - Homological functors on modules (Tor, Ext, etc.) 13D25 - Complexes

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