Kunz Regularity Criterion via algebraic entropy

TL;DR

This paper applies the concept of algebraic entropy to prove the Kunz Regularity Criterion for contracting self-maps of finite length in Noetherian local rings across all characteristics, extending previous results with a new approach.

Contribution

It introduces a novel application of algebraic entropy to establish the Kunz Regularity Criterion in a more general setting.

Findings

Proves Kunz Regularity Criterion using algebraic entropy.

Extends Kunz Criterion to all characteristics for contracting self-maps.

Provides a new method differing from previous approaches by Avramov, Iyengar, and Miller.

Abstract

In arXiv:1109.6438v1 [math.AG] we introduced and studied a notion of algebraic entropy. In this paper we will give an application of algebraic entropy in proving Kunz Regularity Criterion for all contracting self-maps of finite length of Noetherian local rings in arbitrary characteristic. Some conditions of Kunz Criterion have already been extended to the general case by Avramov, Iyengar and Miller in arXiv:math/0312412v2 [math.AC], using different methods.