GL-algebras in positive characteristic I: the exterior algebra

TL;DR

This paper investigates the structure of GL-equivariant modules over the infinite exterior algebra in positive characteristic, establishing a shift theorem and bounds on regularity, with finiteness results for local cohomology.

Contribution

It introduces a shift theorem for GL-equivariant modules over the infinite exterior algebra in positive characteristic and derives bounds on Castelnuovo--Mumford regularity.

Findings

Established a shift theorem similar to Nagpal's

Derived a Church--Ellenberg type bound for regularity

Proved finiteness results for local cohomology

Abstract

We study the category of GL-equivariant modules over the infinite exterior algebra in positive characteristic. Our main structural result is a shift theorem a la Nagpal. Using this, we obtain a Church--Ellenberg type bound for the Castelnuovo--Mumford regularity. We also prove finiteness results for local cohomology.