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Fiber functors for finite symmetric tensor categories in positive characteristic
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Abstract
We prove the finite case of the Benson–Etingof–Ostrik conjecture: every finite symmetric tensor category over an algebraically closed field k of characteristic p > 0 admits a k-linear exact faithful strong symmetric monoidal functor to a finite higher Verlinde category $\mathop{\mathrm{Ver}}\nolimits _{p^n}(k)$. The result includes characteristic two, and the level n may depend on the category.
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Collected automatically by AI tools (Claude Opus 5.5 and GPT-6 Astra, 2026-10-21) and not checked by a person. May be wrong or incomplete. Report an error.
Comments and discussion
- David Roberts, Comment on “How can one contact the authors of OpenAI's October 2026 mathematics release regarding corrections or missing references?” (MathOverflow, 2026-10-09). Roberts points to Coulembier and Flake's arXiv:2610.04096 as a pre-release paper proving the tensor-category conjecture also addressed by the OpenAI manuscript.
- ul1ses (forum user), post #11 in "First look at mathematics manuscripts from an internal frontier model at OpenAI" (OpenAI Developer Community, 2026-10-12). The post connects this manuscript's finite Benson–Etingof–Ostrik claim to arXiv:2610.04096, which it says "appeared before the publication of the openai paper" and "should be acknowledged in an updated version".
Related prior literature mentioned by others
- Kevin Coulembier, Johannes Flake, The Benson--Etingof--Ostrik conjecture for finite tensor categories (arXiv:2610.04096, v1 submitted 2 Oct 2026). Proves that every finite symmetric tensor category in positive characteristic fibres over some $\mathrm{Ver}_{p^r}$ (Theorem B), via higher Frobenius functors and a refined splitting statement resolving the Coulembier–Flake Steinberg-tensor-product conjecture (Theorem A), matching this paper's main result and restricted-tilting input; it is not in this paper's bibliography. Its introduction says the main proof ideas were obtained with "GPT-6 Astra" and mentions an independent alternative proof by Alexander Sherman (in preparation).
Elsewhere
- VibeMathed: Problem record
- Emergent Mind: family 208
Independent sites; their content is not reviewed here.
Cite
@misc{OAI:Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026,
author = {{OpenAI}},
title = {{Fiber functors for finite symmetric tensor categories in positive characteristic}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026/paper.pdf}{OAI:Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026}},
year = {2026}
}Family 208: Finite symmetric tensor categories and the Verlinde tower
Proves that every finite symmetric tensor category over an algebraically closed field k of characteristic p > 0 admits a k-linear exact faithful strong symmetric monoidal fiber functor to a higher Verlinde category $\mathrm{Ver}_{p^n}$. The level may depend on the category, and the theorem includes characteristic two, resolving the finite case of the Benson–Etingof–Ostrik conjecture.
This is the only paper in this family.