---
_id: '66339'
abstract:
- lang: eng
  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.
author:
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
citation:
  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>
  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>
  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} }'
  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>.
  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>.'
  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>.
  short: M. Ulirsch, ArXiv:1603.07589 (2016).
date_created: 2026-07-08T07:09:58Z
date_updated: 2026-07-08T09:29:23Z
doi: 10.1016/j.aim.2019.01.008
external_id:
  arxiv:
  - '1603.07589'
language:
- iso: eng
publication: arXiv:1603.07589
status: public
title: Non-Archimedean geometry of Artin fans
type: journal_article
user_id: '82981'
year: '2016'
...