We determine internal characterizations for the case when a tensor category is (super) Tannakian over fields of positive characteristic. This generalizes the corresponding characterizations in characteristic by Deligne. We also explore notions of Frobenius twists in tensor categories in positive characteristic.
"Tannakian categories in positive characteristic." Duke Math. J. 169 (16) 3167 - 3219, 1 November 2020. https://doi.org/10.1215/00127094-2020-0026