GL-equivariance in positive characteristic I: The infinite exterior algebra

Ganapathy, Karthik

doi:10.48550/arxiv.2203.03693

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2022

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“…There has been much work on this in characteristic 0, e.g., [SS1,SS2,Sno]. Only recently have the first serious results been obtained in positive characteristic [Gan1,Gan2]. We hope to see more work in this direction in the future.…”

Section: Introductionmentioning

confidence: 99%

The Geometry of Polynomial Representations

Bik

Draisma

Eggermont

et al. 2022

International Mathematics Research Notices

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We define a GL-variety to be an (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used to study asymptotic properties of invariants like strength and tensor rank and played a key role in two recent proofs of Stillman’s conjecture. We initiate a systematic study of $\textbf {GL}$-varieties and establish a number of foundational results about them. For example, we prove a version of Chevalley’s theorem on constructible sets in this setting.

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Section: Introductionmentioning

confidence: 99%