Reductive group schemes over the Fargues-Fontaine curve

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.