---
_id: '66351'
abstract:
- lang: eng
  text: 'For a complex toric variety $X$ the logarithmic absolute value induces a
    natural retraction of $X$ onto the set of its non-negative points and this retraction
    can be identified with a quotient of $X(\mathbb{C})$ by its big real torus. We
    prove an analogous result in the non-Archimedean world: The Kajiwara-Payne tropicalization
    map is a non-Archimedean analytic stack quotient of $X^{an}$ by its big affinoid
    torus. Along the way, we provide foundations for a geometric theory of non-Archimedean
    analytic stacks, particularly focussing on analytic groupoids and their quotients,
    the process of analytification, and the underlying topological spaces of analytic
    stacks.'
author:
- first_name: Martin
  full_name: Ulirsch, Martin
  last_name: Ulirsch
citation:
  ama: Ulirsch M. Tropicalization is a non-Archimedean analytic stack quotient. <i>arXiv:14102216</i>.
    Published online 2014.
  apa: Ulirsch, M. (2014). Tropicalization is a non-Archimedean analytic stack quotient.
    In <i>arXiv:1410.2216</i>.
  bibtex: '@article{Ulirsch_2014, title={Tropicalization is a non-Archimedean analytic
    stack quotient}, journal={arXiv:1410.2216}, author={Ulirsch, Martin}, year={2014}
    }'
  chicago: Ulirsch, Martin. “Tropicalization Is a Non-Archimedean Analytic Stack Quotient.”
    <i>ArXiv:1410.2216</i>, 2014.
  ieee: M. Ulirsch, “Tropicalization is a non-Archimedean analytic stack quotient,”
    <i>arXiv:1410.2216</i>. 2014.
  mla: Ulirsch, Martin. “Tropicalization Is a Non-Archimedean Analytic Stack Quotient.”
    <i>ArXiv:1410.2216</i>, 2014.
  short: M. Ulirsch, ArXiv:1410.2216 (2014).
date_created: 2026-07-08T07:23:45Z
date_updated: 2026-07-08T07:23:51Z
external_id:
  arxiv:
  - '1410.2216'
language:
- iso: eng
publication: arXiv:1410.2216
status: public
title: Tropicalization is a non-Archimedean analytic stack quotient
type: preprint
user_id: '82981'
year: '2014'
...