
TL;DR
This paper develops a generalized theory of tropicalizations over arbitrary non-archimedean valued fields, connecting algebraic and convex geometry through toric schemes and non-archimedean analysis.
Contribution
It extends fundamental tropical geometry results to more general fields by constructing toric schemes over valuation rings of rank 1.
Findings
Generalization of tropicalization results to arbitrary non-archimedean fields
Development of a theory of toric schemes over valuation rings
Application of non-archimedean analysis techniques
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsIsland Studies and Pacific Affairs
