Finite symmetric tensor categories and the Verlinde tower

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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.

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The paper states

Theorem 1.1

In Fiber functors for finite symmetric tensor categories in positive characteristic, 24 September 2026

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For every prime p, every algebraically closed field k of characteristic p, and every finite symmetric tensor category \mathcal C over k, there are an integer n\geq1 and a fiber functor

\mathcal C\longrightarrow\operatorname{Ver}_{p^n}(k).

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Fiber functors for finite symmetric tensor categories in positive characteristic

24 September 2026, current edition.

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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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