2014/10/08 by Ulirsch, Martin
#14A20 #14T05 #32P05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1410.2216
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(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 Xan 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.