Metric uniformization of morphisms of Berkovich curves via p-adic\n differential equations

2019/01/22 by Baldassarri, Francesco, Velibor Bojković, Bojković, Velibor · 1 citation
Computer Science · Mathematics · #12H25 #14G22 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1901.07644

openalex publication_date 2019/01/22 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

We consider a finite 'etale morphism f:Y \→ X of quasi-smooth Berkovich\ncurves over a complete nonarchimedean non-trivially valued field k, assumed\nalgebraically closed and of characteristic 0, and a skeleton\n\Γ_f=(\Γ_Y,\Γ_X)\n of the morphism f. We prove that \Γ_f radializes f if and only if\n\Γ_X controls the pushforward of the constant p-adic differential\nequation f_*(\O_Y,d_Y).\n Furthermore, when f is a finite 'etale morphism of open unit discs, we\nprove that f is radial if and only if the number of preimages of a point\nx\∈ X, counted without multiplicity, only depends on the radius of the point\nx.\n

Cited by

• Mittag-Leffler problems on Berkovich curves

Related

• Metric uniformization of morphisms of Berkovich curves
• Infinitesimal deformation of p-adic differential equations on Berkovich curves
• Pushforwards of p-adic differential equations
• Continuity and finiteness of the radius of convergence of a p-adic differential equation via potential theory
• Radiality of definable sets