Non-Archimedean geometry of Artin fans Ulirsch, Martin The purpose of this article is to study the role of Artin fans in tropical and non-Archimedean geometry. Artin fans are logarithmic algebraic stacks that can be described completely in terms of combinatorial objects, so called Kato stacks, a stack-theoretic generalization of K. Kato's notion of a fan. Every logarithmic algebraic stack admits a tautological strict morphism $φ_\mathcal{X}:\mathcal{X}\rightarrow\mathcal{A}_\mathcal{X}$ to an associated Artin fan. The main result of this article is that, on the level of underlying topological spaces, the natural functorial tropicalization map of $\mathcal{X}$ is nothing but the non-Archimedean analytic map associated to $φ_\mathcal{X}$ by applying Thuillier's generic fiber functor. Using this framework, we give a reinterpretation of the main result of Abramovich-Caporaso-Payne identifying the moduli space of tropical curves with the non-Archimedean skeleton of the corresponding algebraic moduli space. 2016 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/66339 Ulirsch M. Non-Archimedean geometry of Artin fans. <i>arXiv:160307589</i>. Published online 2016. doi:<a href="https://doi.org/10.1016/j.aim.2019.01.008">10.1016/j.aim.2019.01.008</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2019.01.008 info:eu-repo/semantics/altIdentifier/arxiv/1603.07589 info:eu-repo/semantics/closedAccess