A finiteness condition on local cohomology in positive characteristic

TL;DR

This paper introduces a specific condition on local Cohen-Macaulay F-injective rings in positive characteristic that ensures the top local cohomology module has finitely many Frobenius compatible submodules, advancing understanding of their structure.

Contribution

It establishes a new finiteness condition linking F-injectivity and local cohomology modules in positive characteristic rings.

Findings

Finiteness of Frobenius compatible submodules in top local cohomology

Condition on F-injective rings implying structural properties

Advancement in understanding local cohomology in positive characteristic

Abstract

In this paper we present a condition on a local Cohen-Macaulay F-injective ring of positive characteristic $p > 2$ which implies that its top local cohomology module with support in the maximal ideal has finitely many Frobenius compatible submodules.