Hahn analytification and connectivity of higher rank tropical varieties
Abstract
We show that the tropicalization of a connected variety over a higher rank valued field is a path connected topological space. This establishes an affirmative answer to a question posed by Banerjee. Higher rank tropical varieties are studied as the images of "Hahn analytifications", introduced in this paper. A Hahn analytification is a space of valuations on a scheme over a higher rank valued field. We prove that the Hahn analytification is related to higher rank tropicalization by means of an inverse limit theorem, extending well-known results in the non-Archimedean case. We also establish comparison results between the Hahn analytification and the Huber and Berkovich analytifications, as well as the Hrushovski-Loeser stable completion.
Keywords
Cite
@article{arxiv.1504.07207,
title = {Hahn analytification and connectivity of higher rank tropical varieties},
author = {Tyler Foster and Dhruv Ranganathan},
journal= {arXiv preprint arXiv:1504.07207},
year = {2017}
}
Comments
v2: 19 pages, 1 figure. Minor changes and corrections. To appear in manuscripta mathematica