Gorenstein dimension of modules over homomorphisms
Commutative Algebra
2007-05-23 v2
Abstract
Given a homomorphism of commutative noetherian rings R --> S and an S-module N, it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals sup{m | Tor^R_m(E,N) \noteq 0} where E is the injective hull of the residue field of R. This result is analogous to a theorem of Andr\'e on flat dimension.
Cite
@article{arxiv.math/0504340,
title = {Gorenstein dimension of modules over homomorphisms},
author = {Lars Winther Christensen and Srikanth Iyengar},
journal= {arXiv preprint arXiv:math/0504340},
year = {2007}
}
Comments
14 pp. To appear in J. Pure Appl. Algebra. Also available from http://www.math.unl.edu/~lchristensen3/index.html