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Ring homomorphisms and finite Gorenstein dimension

Published online by Cambridge University Press:  01 September 1997

LL Avramov  and
H-B Foxby
LL Avramov
Affiliation:
Matematisk Institut, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark. E-mail: foxby@math.ku.dk
H-B Foxby
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA. E-mail: avramov@math.purdue.edu
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Abstract

The local structure of homomorphisms of commutative noetherian rings is investigated from the point of view of dualizing complexes. A concept of finite Gorenstein dimension, which substantially weakens the notion of finite flat dimension, is introduced for homomorphisms. It is shown to impose structural constraints, due to a remarkable equivalence of subcategories of the derived category of all modules.

An essential part of this study is the development of relative notions of dualizing complexes and Bass numbers. It is proved that the Bass numbers of local homomorphisms are rigid, extending a known result for local rings. Quasi-Gorenstein homomorphisms are introduced as local homomorphisms that base-change a dualizing complex for the source ring into one for the target. They are shown to have the stability properties of the Gorenstein homomorphism that they generalize.

1991 Mathematics Subject Classification: primary 13H10, 13D23, 14E40; secondary 13C15.

Keywords

G-dimensiondualizing complexesBass numbers
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 75 , Issue 2 , September 1997 , pp. 241 - 270
Copyright
London Mathematical Society 1997

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