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.

Manuscript

Fiber functors for finite symmetric tensor categories in positive characteristic

September 24, 2026 · source · cite as \cite{OAI:Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026}

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.

Result 208 · Algebra. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.