The Benson--Etingof--Ostrik conjecture for finite tensor categories
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.
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BibTeX
@misc{coulembier2026bensonetingofostrik,
title = {{The Benson--Etingof--Ostrik conjecture for finite tensor categories}},
author = {Kevin Coulembier and Johannes Flake},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04096},
eprint = {2610.04096},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04096},
}
RIS
TY - UNPB
TI - The Benson--Etingof--Ostrik conjecture for finite tensor categories
AU - Kevin Coulembier
AU - Johannes Flake
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.04096
UR - https://arxiv.org/abs/2610.04096
AB - 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.
ER -