A guide to tropicalizations
Algebraic Geometry
2012-10-09 v3
Abstract
Tropicalizations form a bridge between algebraic and convex geometry. We generalize basic results from tropical geometry which are well-known for special ground fields to arbitrary non-archimedean valued fields. To achieve this, we develop a theory of toric schemes over valuation rings of rank 1. As a basic tool, we use techniques from non-archimedean analysis.
Cite
@article{arxiv.1108.6126,
title = {A guide to tropicalizations},
author = {Walter Gubler},
journal= {arXiv preprint arXiv:1108.6126},
year = {2012}
}
Comments
62 pages, 1 figure. Thorough revision according to the suggestions of the referee. Changes include Prop. 6.9 and the end of Section 11