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

Dorian Berger

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

Algebraic Geometry 2022-01-13 v2 Number Theory

Authors: Dorian Berger

Abstract

We develop properties of unramified, \'etale 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.

Keywords

Berkovich spaces étale morphisms unramified morphisms smooth morphisms analytification valued fields arithmetic geometry

Cite

@article{arxiv.2112.02907,
  title  = {Espaces de Berkovich sur $\mathbb{Z}$: morphismes \'etales},
  author = {Dorian Berger},
  journal= {arXiv preprint arXiv:2112.02907},
  year   = {2022}
}

Comments

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