Cohen Factorizations: Weak Functoriality and Applications
arXiv:1205.2119
Abstract
We investigate Cohen factorizations of local ring homomorphisms from three perspectives. First, we prove a "weak functoriality" result for Cohen factorizations: certain morphisms of local ring homomorphisms induce morphisms of Cohen factorizations. Second, we use Cohen factorizations to study the properties of local ring homomorphisms (Gorenstein, Cohen-Macaulay, etc.) in certain commutative diagrams. Third, we use Cohen factorizations to investigate the structure of quasi-deformations of local rings, with an eye on the question of the behavior of CI-dimension in short exact sequences.
25 pages, uses xypic. In V.2, statement of Theorem C is modified, Example 3.5 is new, and Remarks 4.10 and 5.3 are new. v.3 only small editorial changes to 4.10 and acknowledgements. Final version to appear in JPAA