Reductive group schemes over the Fargues-Fontaine curve

2017/03/02 by Johannes Anschütz, Anschütz, Johannes
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11S31 #11S37 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1703.00700

openalex publication_date 2017/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Generically isotropic reductive group schemes are locally isotropic
• On tamely ramified \mathcal G-bundles on curves
• G-bundles on the absolute Fargues-Fontaine curve
• Groupes Classiques
• Flasque resolutions of reductive group schemes