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The geometry of polynomial representations in positive characteristic

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arxiv 2406.07415 v1 pith:4NH4HGBP submitted 2024-06-11 math.AG math.RT

Arthur Bik , Jan Draisma , Andrew Snowden This is my paper · ORCID
classification math.AGmath.RT
keywords characteristicpolynomialpositivetheoryvarietyapplicationchevalleyconstructible
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. GL-algebras in positive characteristic III: the divided power algebra

    math.AC 2026-08 conditional novelty 7.0 of 10

    The divided power algebra Div(k^∞) over a field of characteristic p is GL-coherent, and its bounded derived category of finitely presented modules has a semi-orthogonal decomposition into pieces generated by D^(r) ⊗ L_λ.

  2. Strength and partition rank under limits and field extensions

    math.AG 2025-02 conditional novelty 6.0 of 10

    For fixed degree d, strength and partition rank over any field are bounded by O(r^{d-1}) (plus a log factor on finite fields) in terms of their border rank analogues.

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