Asymptotic behavior of dimensions of syzygies
Commutative Algebra
2011-10-21 v1
Abstract
Let R be a commutative noetherian local ring, and M a finitely generated R-module of infinite projective dimension. It is well-known that the depths of the syzygy modules of M eventually stabilize to the depth of R. In this paper, we investigate the conditions under which a similar statement can be made regarding dimension. In particular, we show that if R is equidimensional and the Betti numbers of M are eventually non-decreasing, then the dimension of any sufficiently high syzygy module of M coincides with the dimension of R.
Keywords
Cite
@article{arxiv.1110.4582,
title = {Asymptotic behavior of dimensions of syzygies},
author = {Kristen A. Beck and Micah J. Leamer},
journal= {arXiv preprint arXiv:1110.4582},
year = {2011}
}
Comments
8 pages; to appear in Proc. Amer. Math. Soc