Hilbert-Kunz multiplicity of binoids

TL;DR

This paper proves that for a broad class of finitely generated binoids, the Hilbert-Kunz multiplicity is always a rational number and does not depend on the characteristic of the base field.

Contribution

It establishes the rationality and characteristic-independence of Hilbert-Kunz multiplicity for finitely generated semipositive cancellative reduced binoids.

Findings

Hilbert-Kunz multiplicity is rational for these binoids.

The multiplicity is independent of the characteristic.

The result applies in a broad combinatorial setting.

Abstract

We prove in a broad combinatorial setting, namely for finitely generated semipositive cancellative reduced binoids, that the Hilbert-Kunz multiplicity is a rational number independent of the characteristic.