A Field of Generalised Puiseux Series for Tropical Geometry
Thomas Markwig
TL;DR
This paper introduces a new algebraically closed and complete field of generalized Puiseux series with real-valued valuation, proposing it as a suitable base field for tropical geometry applications.
Contribution
The paper constructs and analyzes a novel field of generalized Puiseux series with real valuation, expanding the tools available for tropical geometry.
Findings
The field is algebraically closed.
The field is complete with respect to its valuation.
It has a real-valued valuation group.
Abstract
In this paper we define a field K of characteristic zero with valuation whose value group is the real numbers, and we show that this field of generalised Puiseux series is algebraically closed and complete with respect to the norm induced by its valuation. We consider this field to be a good candidate for the base field for tropical geometry.
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
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems