Tropicalization is a non-Archimedean analytic stack quotient
Martin Ulirsch

TL;DR
This paper establishes that the Kajiwara-Payne tropicalization map for non-Archimedean analytic spaces can be understood as a stack quotient, extending classical results from complex toric varieties to the non-Archimedean setting.
Contribution
It introduces a geometric framework for non-Archimedean analytic stacks, including groupoids and quotients, and proves the tropicalization map as a stack quotient.
Findings
Tropicalization map is a non-Archimedean analytic stack quotient.
Develops foundations for non-Archimedean analytic stacks.
Provides a geometric perspective on tropicalization in non-Archimedean geometry.
Abstract
For a complex toric variety the logarithmic absolute value induces a natural retraction of onto the set of its non-negative points and this retraction can be identified with a quotient of 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 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.
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