English

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.

Keywords

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

R2 v1 2026-06-24T11:48:09.497Z