论文标题
在热带曲线上的半场扩展和GALOIS覆盖物的GALOIS动作
Galois actions for semifield extensions and Galois coverings on tropical curves
论文作者
论文摘要
对于半场扩展$ t /s $，如果$（1）$（1）$ $ g $ -g $ -invariant $ t $的$ g $ t $是$ t $的$ g $ in $ t $是$ s $ s $ s $ s $和$ g $的$ g $的$ g $ - invariant usemifield，其不变半ive偶会相等的$ g $。 We show that for a finite harmonic morphism between tropical curves $φ: \varGamma \to \varGamma^{\prime}$ and an isometric action of a finite group $G$ on $\varGamma$, $φ$ is $G$-Galois if and only if the natural action of $G$ on the rational function semifield $ \ vargamma的$ \ vargamma $ $ \ vargamma $ $ \ vargamma $是由$ g $在$ \ \ vargamma $上引起的$ \ vargamma $的$ \ operatorName {rat}（\ vargamma）$ $ \ vargamma $是$ \ vargamma $是$ \ vargamma $是$ \ vargamma $是$ \ vargamma $是$ \ vargamma $是$ \ vargamma $是$ \ vargamma $是$ \ vargamma $是$ \ vargamma $是$ \ vargamma $ is galois φ^{\ ast}（\ operatorName {rat}（\ vargamma^{\ prime}））$，其中$φ^{\ ast}（\ propatatorname {rat} $ \ operatatorName {rat}（\ vargamma^{\ prime}）$ by $φ$。
For a semifield extension $T /S$, an action of a finite group $G$ on $T$ is Galois if $(1)$ the $G$-invariant subsemifield of $T$ is $S$ and $(2)$ subgroups of $G$ whose invariant semifields coincide are equal. We show that for a finite harmonic morphism between tropical curves $φ: \varGamma \to \varGamma^{\prime}$ and an isometric action of a finite group $G$ on $\varGamma$, $φ$ is $G$-Galois if and only if the natural action of $G$ on the rational function semifield $\operatorname{Rat}(\varGamma)$ of $\varGamma$ induced by the action of $G$ on $\varGamma$ is Galois for the semifield extension $\operatorname{Rat}(\varGamma) / φ^{\ast}(\operatorname{Rat}(\varGamma^{\prime}))$, where $φ^{\ast}(\operatorname{Rat}(\varGamma^{\prime}))$ stands for the pull-back of $\operatorname{Rat}(\varGamma^{\prime})$ by $φ$.
