Year: 2026
Type: preprint
Abstract: We prove that every finite symmetric tensor category over an algebraically closed field of positive characteristic admits a symmetric tensor functor to a higher Verlinde category. This was conjectured for arbitrary symmetric tensor categories of moderate growth by Benson, Etingof and Ostrik. The proof uses higher Frobenius functors, introduced by the authors in [CF1]. The main effort is directed towards a proof of a conjecture from [CF1] about thick tensor ideals in the representation category of elementary abelian $p$-groups, which implies that the higher Frobenius functors are symmetric monoidal. In fact, we prove a refinement of the latter conjecture that relates tensoring with restricted Steinberg modules to an iterated generalised cohomology of modules of elementary abelian $p$-groups.
Source: arXiv (Cornell University)
Authors: Coulembier, Kevin, Flake, Johannes
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220705236