math.RT — Representation Theory
The Benson-Etingof-Ostrik conjecture
We prove the conjecture of Benson--Etingof--Ostrik (2023): every symmetric tensor category of moderate growth over an algebraically closed field of positive characteristic admits a symmetric tensor functor to a higher Verlinde category, possibly of infinite height. Using maximal nilpotence and geometric reductivity, we reduce the problem to proving that finitely generated maximally nilpotent tensor categories are finite. The main ingredients are the construction of generic points using alternating norms and a Frobenius reduction of the fundamental coend to an ordinary Hopf subalgebra.
Primarily AI-generated textHuman understanding: some partsBenson-Etingof-OstrikTensor categoriesfiber functorspositive characteristic