A fully faithful p-adic Riemann-Hilbert functor for coadmissible D-cap-modules

2025/06/14 by Finn Wiersig, Wiersig, Finn
Medicine · #14C30 #14F10 #14G22 #14G45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2506.12601

openalex publication_date 2025/06/14 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

This article establishes a Riemann-Hilbert correspondence in rigid-analytic geometry. We construct an explicit solution functor and prove that it is fully faithful on Ardakov-Wadsley's coadmissible D-cap-modules. For vector bundles with flat connection, our functor is canonically identified with Scholze's horizontal sections functor.

Citations

• Auslander regularity of completed rings of p-adic differential operators
• Global sections of equivariant line bundles on the p-adic upper half plane
• Galois and Pro-étale Cohomology of Overconvergent de Rham Period Rings
• Six operations for D-cap-modules on rigid analytic spaces
• Extending meromorphic connections to coadmissible D-cap-modules
• D-modules on rigid analytic spaces II: Kashiwara's equivalence
• D-modules on rigid analytic spaces
• p-adic Hodge theory for rigid-analytic varieties
• Un théorème de Beilinson-Bernstein pour les D-modules arithmétiques
• U(g)-finite locally analytic representations
• Locally analytic distributions and p-adic representation theory, with applications to GL₂

Related

• Galois and Pro-étale Cohomology of Overconvergent de Rham Period Rings
• Six operations for D-cap-modules on rigid analytic spaces
• A Proper Mapping Theorem for coadmissible D-cap-modules
• Extending meromorphic connections to coadmissible D-cap-modules
• A Topological Reconstruction Theorem for D^∞-Modules