Cohen–Macaulay Properties of Ring Homomorphisms

AbstractNumerical invariants which measure the Cohen–Macaulay character of homomorphismsϕ:R→Sof 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 conceptual 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