2 citations · 4 across the 11 of their papers we have counts for
13 papers
Congruence spectra and geometric reconstruction of -algebras
JuAe Song
We develop a geometric theory of congruence spectra for semirings. We define the congruence spectrum for a semiring as the set of prime congruences on it, equip it with the Zariski…
Tropical curves with parallel rays
JuAe Song
In the previous works, the rational function semifields of abstract tropical curves were characterized. In this paper, we give a contravariant categorical equivalence between the c…
Tropical function fields, finite generation, and faithful tropicalization
Omid Amini, Shu Kawaguchi, JuAe Song
Given an algebraic variety defined over a discrete valuation field and a skeleton of its Berkovich analytification, the tropicalization process transforms function field of the var…
A geometric interpretation of Krull dimensions of -algebras
JuAe Song, Yasuhito Nakajima
We investigate Krull dimensions of semirings and semifields dealt in tropical geometry. For a congruence on a tropical Laurent polynomial semiring $\boldsymbol{T}[X_1^{\pm}, \l…
Finitely generated congruences on tropical rational function semifields
JuAe Song
We prove that the congruence on the tropical rational function semifield in -variables associated with a subset of is finitely generated if and only if th…
Congruences on tropical rational function semifields and tropical curves
JuAe Song
We define tropical rational function semifields and prove that a tropical curve is realized (except for points at infinity…
-algebra homomorphisms between rational function semifields of tropical curves
JuAe Song
We prove that an injective -algebra homomorphism between the rational function semifields of two tropical curves induces a surjective morphism between those tropica…
Galois actions for semifield extensions and Galois coverings on tropical curves
JuAe Song
For a semifield extension , an action of a finite group on is Galois if the -invariant subsemifield of is and subgroups of whose invariant…
Galois correspondence for Galois coverings on tropical curves
JuAe Song
We define Galois coverings on tropical curves for which a Galois correspondence and a universal mapping property hold.
Rational function semifields of tropical curves are finitely generated over the tropical semifield
JuAe Song
We prove that the rational function semifield of a tropical curve is finitely generated as a semifield over the tropical semifield $\boldsymbol{T} := ( \boldsymbol{R} \cup \{ - \in…
Upper bounds of orders of automorphism groups of leafless metric graphs
Yusuke Nakamura, JuAe Song
We prove a tropical analogue of the theorem of Hurwitz: a leafless metric graph of genus has at most automorphisms when ; automorphisms when $g \ge 3…
Galois quotients of metric graphs and invariant linear systems
JuAe Song
For a map between metric graphs and an isometric action on by finite group , is a -Galois covering on $\varGamma…
Generators of invariant linear system on tropical curves for finite isometry group
JuAe Song
For a tropical curve and a finite subgroup of the isometry group of the tropical curve, we prove, extending the work by Haase, Musiker and Yu, that the invariant part of the comple…