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The Benson-Etingof-Ostrik conjecture for finite symmetric tensor categories

Theorem 1.1: every finite symmetric tensor category over an algebraically closed field of characteristic $p>0$ has a fiber functor to a single finite level $\mathrm{Ver}_{p^n}(k)$ , including $p=2$ . Consequences stated: classification of finite incompressible categories (the finite case of Coulembier-Etingof-Ostrik's Conjecture B), uniqueness of the functor in characteristic two via their subterminality theorem, and a generalized Tannakian realization. The full conjecture for non-finite categories of moderate growth is not addressed.

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Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Benson-Etingof-Ostrik conjecture for finite symmetric tensor categories · BEO conjecture, finite case

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VibeMathed record: The Benson-Etingof-Ostrik conjecture for finite symmetric tensor categories

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No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against BEO Conjecture 1.4 as the paper states it; it claims a $k$ -linear exact faithful strong symmetric monoidal functor $\mathcal C\to\mathrm{Ver}_{p^n}(k)$ for every finite symmetric tensor category, every prime including 2, with $n$ depending on $\mathcal C$ . The proof was not refereed and is not formalized. The paper itself limits the claim to finite categories and makes no assertion for general moderate-growth categories.

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The Benson-Etingof-Ostrik conjecture for finite symmetric tensor categories

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