English

G-bundles on the absolute Fargues-Fontaine curve

Number Theory 2022-12-23 v2 Algebraic Geometry

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 vv-stack BunFF\mathrm{Bun}_\mathrm{FF} of vector bundles on the Fargues--Fontaine curve) is canonically equivalent to the category of isocrystals. We deduce a similar result for ``GG-bundles on the absolute Fargues--Fontaine curve'' for some reductive group GG as well as for sections of BunFF\mathrm{Bun}_\mathrm{FF} over classifying stacks for locally profinite groups.

Keywords

Cite

@article{arxiv.1606.01029,
  title  = {G-bundles on the absolute Fargues-Fontaine curve},
  author = {Johannes Anschütz},
  journal= {arXiv preprint arXiv:1606.01029},
  year   = {2022}
}

Comments

8 pages, completely rewritten version