Ring Homomorphisms and Finite Gorenstein Dimension |
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Authors: | Avramov, LL Foxby, H-B |
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Affiliation: | Department of Mathematics, Purdue University West Lafayette, IN 47907-1395, USA. E-mail: avramov{at}math.purdue.edu Matematisk Institut, Universitetsparken 5 DK-2100 Copenhagen Ø, Denmark. E-mail: foxby{at}math.ku.dk |
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Abstract: | The local structure of homomorphisms of commutative noetherianrings is investigated from the point of view of dualizing complexes.A concept of finite Gorenstein dimension, which substantiallyweakens the notion of finite flat dimension, is introduced forhomomorphisms. It is shown to impose structural constraints,due to a remarkable equivalence of subcategories of the derivedcategory of all modules. An essential part of this study is the development of relativenotions of dualizing complexes and Bass numbers. It is provedthat the Bass numbers of local homomorphisms are rigid, extendinga known result for local rings. Quasi-Gorenstein homomorphismsare introduced as local homomorphisms that base-change a dualizingcomplex for the source ring into one for the target. They areshown to have the stability properties of the Gorenstein homomorphismthat they generalize. 1991 Mathematics Subject Classification:primary 13H10, 13D23, 14E40; secondary 13C15. |
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Keywords: | G-dimension dualizing complexes Bass numbers |
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