On the Ext Analog of the Euler Characteristic
Commutative Algebra
2025-04-10 v1
Abstract
The Euler form is an Ext analog of the Euler characteristic, and in this paper we study the Euler form and give some applications. The first being a question of Jorgensen, which bounds the projective dimension of a module over a complete intersection by using the vanishing of self extensions. Our second application uses the Euler form to yield a new result involving the vanishing of the higher Herbrand difference. Along the way we translate some of our results to the graded setting.
Cite
@article{arxiv.2504.06450,
title = {On the Ext Analog of the Euler Characteristic},
author = {Benjamin Katz and Andrew J. Soto Levins},
journal= {arXiv preprint arXiv:2504.06450},
year = {2025}
}