2024/09/06 by Itaï Ben Yaacov, Pablo Destic, Yaacov, Itaï Ben +5
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2409.04570
openalex publication_date 2024/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present foundations of globally valued fields, i.e., of a class of fields with an extra structure, capturing some aspects of the geometry of global fields, based on the product formula. We provide a dictionary between various data defining such extra structure: syntactic (models of some unbounded continuous logic theory), Arakelov theoretic, and measure theoretic. In particular we obtain a representation theorem relating globally valued fields and adelic curves defined by Chen and Moriwaki.