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arXiv · 2504.06450

On the Ext Analog of the Euler Characteristic

Benjamin Katz·Andrew J. Soto Levins
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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.

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Benjamin Katz, Andrew J. Soto Levins. 2025-04-08. On the Ext Analog of the Euler Characteristic. https://arxiv.org/abs/2504.06450

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