G-gerbes on perfectoid spaces

2025/11/19 by Long, Xiaohuan, Wang, Yibin, Wu, Xiangdong +1
Mathematics · #14F20 #14G22 #14G45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2511.15126

openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

Let K be a complete non-archimedean field over ℚ_p, G be a rigid group over K, and X be a perfectoid space over K. We consider the natural morphism of sites ν: X_v → X_\mathrm\acuteet. It is known from work of Heuer that the direct image functor ν_* induces an equivalence of the categories of G-torsors. In this article, we show that there is an equivalence of 2-categories of G-gerbes on these two topologies.

Citations

• A Hodge--Tate decomposition with rigid analytic coefficients
• p-adic Simpson correspondences for principal bundles in abelian settings
• Line bundles on perfectoid covers: case of good reduction
• Higher Topos Theory

Related

• G-torsors on perfectoid spaces
• Differentiable Categories, gerbes and G-structures
• Geometric equivalence among smooth map germs
• Classification of nondegenerate G-categories (with an appendix written jointly with Germán Stefanich)
• Characterizing perfectoid covers of abelian varieties