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Summary: RING HOMOMORPHISMS AND FINITE GORENSTEIN DIMENSION
Luchezar L. Avramov and Hans{Bj rn Foxby
Contents
Introduction
1. Homological algebra
2. Dualizing complexes
3. Dualizing equivalences
4. Gorenstein dimension
5. Relative dualizing complexes: Properties
6. Relative dualizing complexes: Proofs
7. Bass numbers of local homomorphisms
8. Quasi-Gorenstein homomorphisms
References
Introduction
This paper, in which all rings are commutative and noetherian, is devoted to the study
of the local structure of ring homomorphisms.
Given a ring homomorphism ' : R ! S, various numerical invariants have been at-
tached in [8], [5], [6], to its localizations ' q : R q\R ! S q at prime ideals q of S. Some of
these numbers, like dimension, depth, or type, express quantitative characteristics of ';
others, like Cohen{Macaulay defect, or complete intersection defect, capture its qualita-
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