4,492 research outputs found
Quasi-complete intersection homomorphisms
Extending a notion defined for surjective maps by Blanco, Majadas, and
Rodicio, we introduce and study a class of homomorphisms of commutative
noetherian rings, which strictly contains the class of locally complete
intersection homomorphisms, while sharing many of its remarkable properties.Comment: Final version, to appear in the special issue of Pure and Applied
Mathematics Quarterly dedicated to Andrey Todorov. The material in the first
four sections has been reorganized and slightly expande
Ascent Properties of Auslander Categories
Let R be a homomorphic image of a Gorenstein local ring. Recent work has
shown that there is a bridge between Auslander categories and modules of finite
Gorenstein homological dimensions over R.
We use Gorenstein dimensions to prove new results about Auslander categories
and vice versa. For example, we establish base change relations between the
Auslander categories of the source and target rings in a homomorphism R -> S of
finite flat dimension.Comment: Minor corrections; example added; 30 pp. To appear in Canad. J. Math.
Also available from authors' homepages
http://www.math.unl.edu/~lchristensen3/publications.html and
http://home.imf.au.dk/holm/publications.htm
Homology over local homomorphisms
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 f: 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.Comment: To appear in the American Journal of Mathematics; new version has
minor changes in the presentation; table of content removed; 52 page
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