GL-algebras in positive characteristic I: the exterior algebra

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.

27 pages; change in title and other minor improvements

References in corpus (3)

• The geometry of polynomial representations
• Universality of high-strength tensors
• Sp-equivariant modules over polynomial rings in infinitely many variables

Cited by in corpus (1)

• GL-algebras in positive characteristic II: the polynomial ring