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arXiv · 2112.02907

Espaces de Berkovich sur $\mathbb{Z}$: morphismes étales

Dorian Berger
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Abstract

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.

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Dorian Berger. 2022-01-12. Espaces de Berkovich sur $\mathbb{Z}$: morphismes étales. https://arxiv.org/abs/2112.02907

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