The geometry of polynomial representations in positive characteristic

A $\mathbf{G}\mathbf{L}$-variety is a (typically infinite dimensional) variety modeled on the polynomial representation theory of the general linear group. In previous work, we studied these varieties in characteristic 0. In this paper, we obtain results in positive characteristic: for example, we prove a version of Chevalley’s theorem on constructible sets. We give an application of our theory to strength of polynomials.