G-torsors over a Dedekind scheme

TL;DR

This paper establishes the equivalence of three perspectives on G-torsors over Dedekind schemes and demonstrates that the category of G-torsors on certain curves forms an Artin stack, advancing the understanding of their geometric structure.

Contribution

It proves the equivalence of three viewpoints of G-torsors over Dedekind schemes and shows the associated category forms an Artin stack, linking torsors to algebraic stack theory.

Findings

Equivalence of three perspectives on G-torsors over Dedekind schemes

The category of G-torsors on a regular proper curve is an Artin stack

The stack is locally of finite presentation over the base field

Abstract

We prove the equivalence of three "points of view" of the notion of a G-torsor when the base scheme is a Dedekind scheme. As an application, we show that the fibered category of G-torsors on a regular proper curve over a field k is an Artin stack locally of finite presentation over k.