# Reductive group schemes over the Fargues-Fontaine curve

## TL;DR

This paper classifies reductive group schemes over the Fargues-Fontaine curve for any non-archimedean local field, extending existing theorems to equal characteristic and providing a classification of torsors via a generalized Kottwitz set.

## Contribution

It introduces a classification of reductive group schemes over the Fargues-Fontaine curve using isocrystals and generalizes Kottwitz' set B(G) for torsors, extending Fargues' theorem to equal characteristic.

## Key findings

- Classification of reductive group schemes over the Fargues-Fontaine curve.
- Extension of Fargues' theorem to equal characteristic.
- Generalization of Kottwitz' set B(G) for torsors.

## Abstract

For an arbitrary non-archimedean local field we classify reductive group schemes over the corresponding Fargues-Fontaine curve by group schemes over the category of isocrystals. We then classify torsors under such reductive group schemes by a generalization of Kottwitz' set B(G). In particular, we extend a theorem of Fargues on torsors under constant reductive groups to the case of equal characteristic.