Document Type
Article
Date
9-9-2004
Disciplines
Mathematics
Description/Abstract
The notions of Betti numbers and of Bass numbers of a finite module N over a local ring R are extended to modules that are only assumed to be finite over S, for some local homomorphism phi: R -> S. Various techniques are developed to study the new invariants and to establish their basic properties. In several cases they are computed in closed form. Applications go in several directions. One is to identify new classes of finite R-modules whose classical Betti numbers or Bass numbers have extremal growth. Another is to transfer ring theoretical properties between R and S in situations where S may have infinite flat dimension over R. A third is to obtain criteria for a ring equipped with a `contracting' endomorphism - such as the Frobenius endomorphism - to be regular or complete intersection; these results represent broad generalizations of Kunz's characterization of regularity in prime characteristic.
Recommended Citation
Avramov, Luchezar L.; Iyengar, Srikanth; and Miller, Claudia, "Homology over Local Homomorphisms" (2004). Mathematics - All Scholarship. 11.
https://surface.syr.edu/mat/11
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript if from arXiv.org, for more information see http://arxiv.org/abs/math/0312412