Extensions and torsors for finite group schemes

TL;DR

This paper provides an explicit framework for understanding and computing with central extensions, torsors, and isomorphism classes of finite commutative group schemes, advancing the algebraic understanding of these structures.

Contribution

It introduces a detailed description of the category of central extensions and a computational framework for finite commutative group schemes and their torsors.

Findings

Explicit description of the category of central extensions

Framework for computing with torsors under finite commutative group schemes

Enhanced understanding of isomorphism classes of these objects

Abstract

We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite commutative group schemes, torsors under such group schemes and groups of isomorphism classes of these objects.