2022/09/15 by Linus Hamann, Hamann, Linus
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2209.07495
openalex publication_date 2022/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a smooth quasi-projective variety over the Fargues-Fontaine curve. Namely, we show how to use their criterion to deduce an analogue for spaces of sections of a smooth Artin stack over the (schematic) Fargues-Fontaine curve obtained by taking the stack quotient of a smooth quasi-projective variety by the action of a linear algebraic group. As an application, we show various moduli stacks appearing in the Fargues-Scholze geometric Langlands program are cohomologically smooth Artin v-stacks and compute their ℓ-dimensions.