Mittag-Leffler problems on Berkovich curves

2019/01/22 by Velibor Bojković, Bojković, Velibor
Mathematics · #14G22 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1901.07650

openalex publication_date 2019/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a quasi-smooth Berkovich curve X admitting a finite triangulation, finitely many disjoint open annuli A₁,…,A_n in X that are not precompact, and for each i=1,…, n, an analytic function f_i (resp. differential form σ_i) convergent on A_i, we provide a criterion for when there exists an analytic function f (resp. a differential form σ) on X inducing the functions f_i (resp. differentials σ_i). Along the way we reprove residue theorem for differentials on smooth Berkovich curves that admit finite triangulations.

Citations

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

Related

• La structure des courbes analytiques
• Infinitesimal deformation of p-adic differential equations on Berkovich curves
• Topology and Geometry of the Berkovich Ramification Locus for Rational Functions
• Cohomological Obstructions for Mittag-Leffler Problems
• Berkovich curves and Schottky uniformization