# Local triviality for G-torsors

## TL;DR

This paper proves that under certain conditions, G-torsors over a proper flat curve are locally trivial in the Zariski topology if they are trivial on the closed fiber, extending understanding of torsor triviality.

## Contribution

It establishes local triviality of G-torsors over proper flat curves in the Zariski topology under mild assumptions, generalizing previous results.

## Key findings

- G-torsors trivial on closed fiber are Zariski-locally trivial
- Results apply to reductive group schemes over proper flat curves
- Advances understanding of torsor triviality in algebraic geometry

## Abstract

Let C $\rightarrow$ Spec(R) be a relative proper flat curve over an henselian base. Let G be a reductive C-group scheme. Under mild technical assumptions, we show that a G-torsor over C which is trivial on the closed fiber of C is locally trivial for the Zariski topology.