A p-adic Simpson correspondence for singular rigid-analytic varieties

2025/12/24 by Hanlin Cai, Zeyu Liu, Cai, Hanlin +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2512.21418

openalex publication_date 2025/12/24 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

Abstract

Let C be a complete, algebraically closed non-archimedean extension of ℚ_p, and X be a proper rigid-analytic variety over C. We show that the category of pro-étale vector bundles on X is equivalent to the category of Higgs bundles on the \eh-site of X, thereby generalizing the work of Faltings and Heuer to arbitrary proper rigid-analytic varieties.

Citations

• Higher F-injective singularities
• A p-adic Simpson correspondence for smooth proper rigid varieties
• Rational p-adic Hodge theory for rigid-analytic varieties
• Moduli spaces in p-adic non-abelian Hodge theory
• Almost coherent modules and almost coherent sheaves
• Hodge-Tate decomposition for non-smooth spaces
• Etale cohomology of diamonds
• Relative p-adic Hodge theory, II: Imperfect period rings
• Foundations of Rigid Geometry I
• Differential forms in the h-topology
• Higher Topos Theory
• Nonabelian Hodge Theory in Characteristic p

Related

• A p-adic Simpson correspondence for smooth proper rigid varieties
• Moduli spaces in p-adic non-abelian Hodge theory
• The small p-adic Simpson correspondence in terms of moduli spaces
• Line bundles on rigid spaces in the v-topology
• Vector bundles with numerically flat reduction on rigid analytic varieties and p-adic local systems