The geometry of polynomial representations in positive characteristic

TL;DR

This paper extends the theory of $ extbf{GL}$-varieties to positive characteristic, proving key theorems like Chevalley's and applying the results to polynomial strength analysis.

Contribution

It introduces new results for $ extbf{GL}$-varieties in positive characteristic, including a Chevalley-type theorem and applications to polynomial strength.

Findings

Proved a version of Chevalley's theorem in positive characteristic.

Established connections between $ extbf{GL}$-varieties and polynomial strength.

Extended previous characteristic 0 results to positive characteristic.

Abstract

A $\mathbf{GL}$-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.