Harish-Chandra pairs for algebraic affine supergroup schemes over an arbitrary field

TL;DR

This paper establishes an equivalence between Harish-Chandra pairs and algebraic affine supergroup schemes over any field with characteristic not equal to 2, and applies this to classify certain types of supergroup schemes.

Contribution

It introduces Harish-Chandra pairs over arbitrary fields and proves their categorical equivalence to algebraic affine supergroup schemes, extending previous results to positive characteristic.

Findings

Categorical anti-equivalence between Harish-Chandra pairs and supergroup schemes

Characterization of simply connected supergroup schemes in positive characteristic

Classification of unipotent and linearly reductive supergroup schemes

Abstract

Over an arbitrary field of characteristic $\ne 2$, we define the notion of Harish-Chandra pairs, and prove that the category of those pairs is anti-equivalent to the category of algebraic affine supergroup schemes. The result is applied to characterize some classes of affine supergroup schemes such as those which are (a) simply connected, (b) unipotent or (c) linearly reductive in positive characteristic.