Tannakian categories in positive characteristic

Abstract

We determine internal characterisations for when a tensor category is (super) tannakian, for fields of positive characteristic. This generalises the corresponding characterisations in characteristic zero by P. Deligne. We also explore notions of Frobenius twists in tensor categories in positive characteristic.

v2: with appendix working out the details of a letter from Deligne to Vasiu v3: some typos corrected v4: correction in characterisation super tannakian categories

Cited by in corpus (5)

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• Monoidal abelian envelopes and a conjecture of Benson--Etingof
• Finite symmetric algebras in tensor categories and Verlinde categories of algebraic groups
• Classification of Non-Degenerate Symmetric Bilinear and Quadratic Forms in the Verlinde Category ${\mathrm{Ver}}_4^{+}$
• The Steinberg Tensor Product Theorem for General Linear Group Schemes in the Verlinde Category