Espaces de Berkovich sur $\mathbb{Z}$: morphismes étales
We develop properties of unramified, étale and smooth morphisms between Berkovich spaces over $\mathbb{Z}$. 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.
math.AG↗