On the Local Cohomology of Reflexive Modules of Rank One over Normal Semigroup Rings

TL;DR

This paper characterizes the local cohomology of rank one reflexive modules over normal semigroup rings and connects the classification of maximal Cohen-Macaulay modules to solving linear inequalities.

Contribution

It provides a description of local cohomology for these modules and links the classification problem to linear inequality solutions.

Findings

Local cohomology of rank one reflexive modules is explicitly described.

Classification of maximal Cohen-Macaulay modules reduces to solving linear inequalities.

The approach offers a new perspective on module classification over semigroup rings.

Abstract

In this work we describe the local cohomology of reflexive modules of rank one over normal semigroup rings with respect to monomial ideals. Using our description we show that the problem of classifying maximal Cohen-Macaulay modules of rank one can be rephrased in terms of finding integral solutions to certain sets of linear inequalities.