On symmetric fusion categories in positive characteristic

TL;DR

This paper explores the extension of Deligne's theorem on super fiber functors to symmetric fusion categories over fields of positive characteristic, providing partial proof for semisimple cases with finitely many simple objects.

Contribution

It proposes a conjectural extension of Deligne's theorem to positive characteristic and proves it for semisimple categories with finitely many simple objects.

Findings

Conjecture extends Deligne's theorem to positive characteristic.

Proof established for semisimple categories with finitely many simple objects.

Lays groundwork for further research in symmetric fusion categories.

Abstract

We propose a conjectural extension to positive characteristic case of a well known Deligne's theorem on the existence of super fiber functors. We prove our conjecture in the special case of semisimple categories with finitely many isomorphism classes of simple objects.