{"type":"journal_article","external_id":{"arxiv":["1603.07589"]},"date_created":"2026-07-08T07:09:58Z","abstract":[{"text":"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.","lang":"eng"}],"publication":"arXiv:1603.07589","citation":{"mla":"Ulirsch, Martin. “Non-Archimedean Geometry of Artin Fans.” <i>ArXiv:1603.07589</i>, 2016, doi:<a href=\"https://doi.org/10.1016/j.aim.2019.01.008\">10.1016/j.aim.2019.01.008</a>.","ama":"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>","bibtex":"@article{Ulirsch_2016, title={Non-Archimedean geometry of Artin fans}, DOI={<a href=\"https://doi.org/10.1016/j.aim.2019.01.008\">10.1016/j.aim.2019.01.008</a>}, journal={arXiv:1603.07589}, author={Ulirsch, Martin}, year={2016} }","apa":"Ulirsch, M. (2016). Non-Archimedean geometry of Artin fans. <i>ArXiv:1603.07589</i>. <a href=\"https://doi.org/10.1016/j.aim.2019.01.008\">https://doi.org/10.1016/j.aim.2019.01.008</a>","ieee":"M. Ulirsch, “Non-Archimedean geometry of Artin fans,” <i>arXiv:1603.07589</i>, 2016, doi: <a href=\"https://doi.org/10.1016/j.aim.2019.01.008\">10.1016/j.aim.2019.01.008</a>.","chicago":"Ulirsch, Martin. “Non-Archimedean Geometry of Artin Fans.” <i>ArXiv:1603.07589</i>, 2016. <a href=\"https://doi.org/10.1016/j.aim.2019.01.008\">https://doi.org/10.1016/j.aim.2019.01.008</a>.","short":"M. Ulirsch, ArXiv:1603.07589 (2016)."},"user_id":"82981","doi":"10.1016/j.aim.2019.01.008","language":[{"iso":"eng"}],"_id":"66339","date_updated":"2026-07-08T09:29:23Z","status":"public","year":"2016","title":"Non-Archimedean geometry of Artin fans","author":[{"id":"114697","full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin"}]}