Tannakian categories in positive characteristic

Kevin Coulembier

doi:10.1215/00127094-2020-0026

Abstract

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 $0$ by Deligne. We also explore notions of Frobenius twists in tensor categories in positive characteristic.

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Kevin Coulembier. "Tannakian categories in positive characteristic." Duke Math. J. 169 (16) 3167 - 3219, 1 November 2020. https://doi.org/10.1215/00127094-2020-0026

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Received: 27 December 2018; Revised: 5 March 2020; Published: 1 November 2020

First available in Project Euclid: 1 October 2020

MathSciNet: MR4167087

Digital Object Identifier: 10.1215/00127094-2020-0026

Subjects:

Primary: 18D10

Secondary: 14L15 , 16D90 , 16T05 , 20C05

Keywords: affine group scheme , fiber functor , Frobenius twist , modular representation theory , tensor category

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