GL-algebras in positive characteristic I: the exterior algebra (2203.03693v2)

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.