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This work aims to investigate the geometry of polynomial representations in positive characteristic.

February 26, 2026Open Access

The geometry of polynomial representations in positive characteristic

Key Points

This work aims to investigate the geometry of polynomial representations in positive characteristic.
Developed a GL-variety framework for studying polynomial representations.
Proved a version of Chevalley's theorem on constructible sets in positive characteristic.
Established significant results for GL-varieties in positive characteristic.
Demonstrated applications related to the strength of polynomials.

Abstract

A 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.

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Authors

Arthur Bik

University of Bern

Jan Draisma

Andrew Snowden

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Algebra Project

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The geometry of polynomial representations in positive characteristic

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