Hilbert-Kunz theory for binoids

TL;DR

This paper extends Hilbert-Kunz theory to binoids, establishing the existence and rationality of Hilbert-Kunz multiplicities in this combinatorial setting, and showing their characteristic independence.

Contribution

It introduces Hilbert-Kunz theory for binoids, proving the existence and rationality of multiplicities and their independence from the characteristic.

Findings

Hilbert-Kunz multiplicity exists for binoids

The multiplicity is a rational number

The multiplicity is characteristic-independent

Abstract

We develop Hilbert-Kunz theory in a combinatorial setting namely for binoids. We show that the Hilbert-Kunz multiplicity for commutative, finitely generated, semipositive, cancellative and reduced binoids exists and is a rational number. This implies that the corresponding Hilbert-Kunz multiplicity for the binoid algebras does not depend on the characteristic.