Total Betti numbers of modules of finite projective dimension
Commutative Algebra
2017-06-06 v2
Abstract
The Buchsbaum-Eisenbud-Horrocks Conjecture predicts that if M is a non-zero module of finite length and finite projective dimension over a local ring R of dimension d, then the i-th Betti number of M is at least d choose i. This conjecture implies that the sum of all the Betti numbers of such a module must be at least 2^d. We prove the latter holds in a large number of cases.
Keywords
Cite
@article{arxiv.1702.02560,
title = {Total Betti numbers of modules of finite projective dimension},
author = {Mark E. Walker},
journal= {arXiv preprint arXiv:1702.02560},
year = {2017}
}
Comments
Version 2 is shorter than the original in order to better focus on the main results. The extra material from version 1 will be posted separately