A stacky nilpotent p-adic Riemann-Hilbert correspondence

2024/11/15 by Yudong Liu, Liu, Yudong, Cuiyan Ma +4
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2411.10165

openalex publication_date 2024/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth rigid variety over C=\mathbb C_p admitting a lift X over B_dR⁺. In this paper, we use the stacky language to prove a nilpotent p-adic Riemann-Hilbert correspondence. After introducing the moduli stack of \mathbb B⁺_dR-local systems and t-connections, we prove that there is an equivalence of the nilpotent locus of the two stacks: RH⁰:LS⁰_X → tMIC⁰_X, where LS⁰_X is the stack of nilpotent \mathbb B⁺_dR-local systems on X_1,v and tMIC⁰_X is the stack of O_X-bundles with integrable t-connection on X_et.

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