$\mathbf{T}$-algebra homomorphisms between rational function semifields of tropical curves

Abstract

We prove that an injective $\mathbf{T}$-algebra homomorphism between the rational function semifields of two tropical curves induces a surjective morphism between those tropical curves, where $\mathbf{T}$ is the tropical semifield $(\mathbf{R}\cup \{-\infty \},\max ,+)$.

18 pages. arXiv admin note: text overlap with arXiv:2110.08091