Rational function semifields of tropical curves are finitely generated over the tropical semifield

2021/12/02 by Song, JuAe
#14T10(Primary) #14T20(Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.01357

Abstract

We prove that the rational function semifield of a tropical curve is finitely generated as a semifield over the tropical semifield \boldsymbolT := ( \boldsymbolR ∪ \ - ∞ \, max, +) by giving a specific finite generating set. Also, we show that for a finite harmonic morphism between tropical curves φ: \varGamma → \varGamma^′, the rational function semifield of \varGamma is finitely generated as a φ^∗(Rat(\varGamma^′))-algebra, where φ^∗(Rat(\varGamma^′)) stands for the pull-back of the rational function semifield of \varGamma^′ by φ.

Related

• Semiring isomorphisms between rational function semifields of tropical curves induce isomorphisms between tropical curves
• Finitely generated congruences on tropical rational function semifields
• \boldsymbolT-algebra homomorphisms between rational function semifields of tropical curves
• Congruences on tropical rational function semifields and tropical curves
• Tropical function fields, finite generation, and faithful tropicalization