Normal and Irreducible Adic Spaces, the Openness of Finite Morphisms and a Stein Factorization
Algebraic Geometry
2020-05-15 v1 Number Theory
Abstract
We transfer several elementary geometric properties of rigid-analytic spaces to the world of adic spaces, more precisely to the category of adic spaces which are locally of (weakly) finite type over a non-archimedean field. This includes normality, irreducibility (in particular irreducible components) and a Stein factorization theorem. Most notably we show that finite morphisms of adic spaces are open under mild assumptions on the base and target space.
Keywords
Cite
@article{arxiv.2005.06859,
title = {Normal and Irreducible Adic Spaces, the Openness of Finite Morphisms and a Stein Factorization},
author = {Lucas Mann},
journal= {arXiv preprint arXiv:2005.06859},
year = {2020}
}