The Improved New Intersection Theorem revisited
Commutative Algebra
2022-10-21 v2
Abstract
We prove a generalized version of Evans and Griffith's Improved New Intersection Theorem: Let I be an ideal in a local ring R. If a finite free R-complex, concentrated in nonnegative degrees, has I-torsion homology in positive degrees, and the homology in degree 0 has an I-torsion minimal generator, then the length of the complex is at least dim R - dim R/I. This improves the bound ht I obtained by Avramov, Iyengar, and Neeman in 2018.
Cite
@article{arxiv.2206.05812,
title = {The Improved New Intersection Theorem revisited},
author = {Lars Winther Christensen and Luigi Ferraro},
journal= {arXiv preprint arXiv:2206.05812},
year = {2022}
}
Comments
Corrected a few typos. Final version, to appear in Michigan Math. J.; 7 pp