The geometry of polynomial representations in positive characteristic

2024/06/11 by Arthur Bik, Bik, Arthur, Jan Draisma +3 · 2 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2406.07415

openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Density of solutions for systems of forms
• Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic

Related

• GL-algebras in positive characteristic II: the polynomial ring
• Arbeitsgemeinschaft: Geometric Representation Theory
• Topics in group schemes and surfaces in positive characteristic
• Relations between some invariants of algebraic varieties in positive characteristic
• On abstract representations of the groups of rational points of\n algebraic groups in positive characteristic