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.
released 2026-09-24 | 3 theorems · 13 lemmas · 22 proofs · 11,262 words |
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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.