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arXiv · 1306.5967

Geometry of totally real Galois fields of degree 4

Yury Kochetkov
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Abstract

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 $\Gamma$ is an infinite union of 3-dimensional polyhedrons. The group $U$ of strictly positive units acts on $\Gamma$: 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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Yury Kochetkov. 2013-06-25. Geometry of totally real Galois fields of degree 4. https://arxiv.org/abs/1306.5967

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