A bound on the Hartshorne-Speiser-Lyubeznik number of semigroup rings

TL;DR

This paper establishes an explicit, computable upper bound for the Hartshorne-Speiser-Lyubeznik number in local cohomology of affine semigroup rings over perfect fields, depending only on characteristic and semigroup properties.

Contribution

It provides the first explicit bound on the Hartshorne-Speiser-Lyubeznik number for semigroup rings, linking algebraic invariants to combinatorial data.

Findings

Derived a bound depending on characteristic and semigroup properties

Bound is explicit and computable

Applicable to local cohomology of affine semigroup rings

Abstract

In this paper we prove an explicit, computable upper bound on the Hartshorne-Speiser-Lyubeznik number of the local cohomology of a pointed, affine semigroup ring over a perfect field of positive characteristic. This bound depends only on the characteristic of the ring and properties of the semigroup.