2021/12/06 by Dorian Berger, Berger, Dorian
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2112.02907
openalex publication_date 2021/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop properties of unramified, étale and smooth morphisms between Berkovich spaces over ℤ. We prove that they satisfy properties analogous to those of morphisms of schemes and we provide analytification criteria. Our results hold for any valued field, rings of integers of a number field and discrete valuation rings. Those cases are treated by a unified way.