四次全实伽罗瓦域的几何
Geometry of totally real Galois fields of degree 4
摘要：
我们将考虑一个4次全实伽罗瓦域$K$作为线性坐标空间$\mathbb{Q}^4\subset\mathbb{R}^4$。一个元素$k\in K$称为严格正的，如果它的所有共轭都是正的。严格正元素的集合是$K$中的凸锥。严格正整元的凸包是该锥的凸子集，其边界$Γ$是三维多面体的无限并。严格正单位的群$U$作用于$Γ$：严格正单位的作用置换多面体。这一行动的基本区是本书的研究对象。我们主要介绍一些有趣的例子。
英文摘要：
We will consider a totally real Galois field $K$ of degree 4 as the linear coordinate space $\mathbb{Q}^4\subset\mathbb{R}^4$. An element $k\in K$ is called strictly positive, if all its conjugates are positive. The set of strictly positive elements is a convex cone in $K$. The convex hull of strictly positive integral elements is a convex subset of this cone and its boundary $Γ$ is an infinite union of 3-dimensional polyhedrons. The group $U$ of strictly positive units acts on $Γ$: the action of a strictly positive unit permutes polyhedrons. Fundamental domains of this action are the object of study in this work. We mainly present some interesting examples.
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