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COHEN--MACAULAY PROPERTIES OF RING HOMOMORPHISMS Luchezar L. Avramov and HansBjrn Foxby
 

Summary: COHEN--MACAULAY PROPERTIES OF RING HOMOMORPHISMS
Luchezar L. Avramov and Hans­Bjørn Foxby
Abstract. Numerical invariants which measure the Cohen--Macaulay character of homo­
morphisms ' : R ! S of noetherian rings are introduced and studied. Comprehensive results
are obtained for homomorphisms which are locally of finite flat dimension. They provide a
point of view from which a variety of phenomena receive a unified treatment. The concep­
tual clarification and technical versatility of this approach leads, among other things, to a
determination of those homomorphisms which preserve the Cohen--Macaulay character of the
rings, to the discovery of new classes of homomorphisms with remarkable stability properties,
and to solutions of some problems on flat homomorphisms, raised by Grothendieck in EGA.
Contents
Introduction
1. Commutative algebra of complexes
2. Codimension and finite projective dimension
3. Cohen--Macaulay defect of a local homomorphism
4. Composition of local homomorphisms
5. Localization
6. Cohen--Macaulay defects of a ring homomorphism
7. Type of a local homomorphism
8. Locally Cohen--Macaulay homomorphisms

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics