2022/11/15 by Quentin Gazda, Gazda, Quentin, Andreas Maurischat +1
Computer Science · Mathematics · #11G09 (Primary) 11R58 #11J93 #14H05 (Secondary) #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #Combinatorics #Crystallography #Discrete mathematics #FOS: Mathematics #Geometry #Graph #Graph isomorphism #Holomorphic and Operator Theory #Inverse #Isomorphism (crystallography) #Lattice (music) #Line graph #Mathematics #Meromorphic function #Morphism #Number Theory (math.NT) #Physics #Pure mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2211.08121
openalex publication_date 2022/11/15 · openalex created_date 2023/02/14 · openalex updated_date 2026/08/05
Let E be an Anderson A-module over ℂ∞. The period lattice of E is related to its module of special functions by means of a non-canonical isomorphism introduced by the authors in [GM21]. In this paper, we explain how a modification of the inverse map is canonical by interpreting it as a residue morphism along the characteristic graph. This phenomenon has already been observed in various situations. The main innovation of this text is that of costability (costable admissible opens, costable site, etc.) which provides a convenient framework to develop the notion of sheaves of E(ℂ∞)-valued meromorphic functions on the rigid analytic plane.