On the Frobenius functor for symmetric tensor categories in positive characteristic

  title={On the Frobenius functor for symmetric tensor categories in positive characteristic},
  author={Pavel Etingof and Victor Ostrik},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={165 - 198}
  • P. EtingofV. Ostrik
  • Published 30 December 2019
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
Abstract We develop a theory of Frobenius functors for symmetric tensor categories (STC) 𝒞 {\mathcal{C}} over a field 𝒌 {\boldsymbol{k}} of characteristic p, and give its applications to classification of such categories. Namely, we define a twisted-linear symmetric monoidal functor F : 𝒞 → 𝒞 ⊠ Ver p {F:\mathcal{C}\to\mathcal{C}\boxtimes{\rm Ver}_{p}} , where Ver p {{\rm Ver}_{p}} is the Verlinde category (the semisimplification of Rep 𝐤 ( ℤ / p ) {\mathop{\mathrm{Rep}}\nolimits_{\mathbf{k… 
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