Limits of tropicalizations
Algebraic Geometry
2016-04-19 v2
Abstract
We give general criteria under which the limit of a system of tropicalizations of a scheme over a nonarchimedean field is homeomorphic to the analytification of the scheme. As an application, we show that the analytification of an arbitrary closed subscheme of a toric variety is naturally homeomorphic to the limit of its tropicalizations, generalizing an earlier result of the third author for quasiprojective varieties.
Keywords
Cite
@article{arxiv.1211.2718,
title = {Limits of tropicalizations},
author = {Tyler Foster and Philipp Gross and Sam Payne},
journal= {arXiv preprint arXiv:1211.2718},
year = {2016}
}
Comments
8 pages; v2: revised argument in proof of main theorem, results unchanged