English

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

R2 v1 2026-06-21T22:36:59.531Z