## $G$-bundles on the absolute Fargues–Fontaine curve

### Volume 207 / 2023

Acta Arithmetica 207 (2023), 351-363
MSC: Primary 14G45; Secondary 13F35.
DOI: 10.4064/aa221222-21-2
Published online: 11 April 2023

#### Abstract

We prove that the category of “vector bundles on the absolute Fargues–Fontaine curve” (more precisely the category of sections over some discrete algebraically closed field of the $v$-stack ${\rm Bun}_{\rm FF}$ of vector bundles on the Fargues–Fontaine curve) is canonically equivalent to the category of isocrystals. We deduce a similar result for “$G$-bundles on the absolute Fargues–Fontaine curve” for some reductive group $G$, as well as for sections of ${\rm Bun}_{\rm FF}$ over classifying stacks for locally profinite groups.