[{"abstract":[{"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.","lang":"eng"}],"publication":"arXiv:1410.2216","citation":{"mla":"Ulirsch, Martin. “Tropicalization Is a Non-Archimedean Analytic Stack Quotient.” <i>ArXiv:1410.2216</i>, 2014.","ama":"Ulirsch M. Tropicalization is a non-Archimedean analytic stack quotient. <i>arXiv:14102216</i>. Published online 2014.","bibtex":"@article{Ulirsch_2014, title={Tropicalization is a non-Archimedean analytic stack quotient}, journal={arXiv:1410.2216}, author={Ulirsch, Martin}, year={2014} }","apa":"Ulirsch, M. (2014). Tropicalization is a non-Archimedean analytic stack quotient. In <i>arXiv:1410.2216</i>.","ieee":"M. Ulirsch, “Tropicalization is a non-Archimedean analytic stack quotient,” <i>arXiv:1410.2216</i>. 2014.","short":"M. Ulirsch, ArXiv:1410.2216 (2014).","chicago":"Ulirsch, Martin. “Tropicalization Is a Non-Archimedean Analytic Stack Quotient.” <i>ArXiv:1410.2216</i>, 2014."},"type":"preprint","external_id":{"arxiv":["1410.2216"]},"date_created":"2026-07-08T07:23:45Z","date_updated":"2026-07-08T07:23:51Z","year":"2014","title":"Tropicalization is a non-Archimedean analytic stack quotient","status":"public","author":[{"full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin"}],"user_id":"82981","language":[{"iso":"eng"}],"_id":"66351"}]