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Ascent Properties of Auslander Categories

Published online by Cambridge University Press:  20 November 2018

Lars Winther Christensen  and
Henrik Holm
Lars Winther Christensen
Affiliation:
Department of Mathematics, University of Britich Columbia, Vancouver, BC, V6T 1Z2,behrend@math.ubc.ca
Henrik Holm
Affiliation:
Department of Mathematics, Middlesex College, University of Western Ontario, London, ON, N6A 5B7, adhill3@uwo.ca
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Abstract

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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 1 , 01 February 2009 , pp. 76 - 108
Copyright
Copyright © Canadian Mathematical Society 2009

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