# Regularity of FI-modules and local cohomology

## TL;DR

This paper proves a conjecture linking the regularity of FI-modules to their local cohomology groups, drawing an analogy to similar relationships in commutative algebra.

## Contribution

It establishes a fundamental connection between regularity and local cohomology in FI-modules, confirming a conjecture by Li and Ramos.

## Key findings

- Proves the conjecture relating FI-module regularity to local cohomology.
- Provides an algebraic framework analogous to commutative algebra.
- Enhances understanding of FI-module structure and properties.

## Abstract

We resolve a conjecture of Li and Ramos that relates the regularity of an FI-module to its local cohomology groups. This is an analogue of the familiar relationship between regularity and local cohomology in commutative algebra.