article Martin Ulirsch author 114697 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 eng 1603.0758910.1016/j.aim.2019.01.008 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>. 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> @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} } 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> 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>. M. Ulirsch, ArXiv:1603.07589 (2016). 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>. 663392026-07-08T07:09:58Z2026-07-08T09:29:23Z