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

Volume 207 / 2023

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


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.


  • Johannes AnschützMathematisches Institut
    Universität Bonn
    53115 Bonn, Germany

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