Finite symmetric tensor categories and the Verlinde tower
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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 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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MANUSCRIPT 01
Fiber functors for finite symmetric tensor categories in positive characteristic
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{Ver}\nolimits _{p^n}(k). The result includes…
Full source 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{Ver}\nolimits _{p^n}(k). The result includes characteristic two, and the level n may depend on the category.
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