F1-schemes and toric varieties

Abstract

This paper contains a loose collection of remarks on F1-schemes. Etale morphisms and universal coverings are introduced. The relation to toric varieties, at least for integral schemes, is clarified.In this paper it is shown that integral F1-schemes of finite type are essentially the same as toric varieties. A description of the F1-zeta function in terms of toric geometry is given. Etale morphisms and universal coverings are introduced.

References in corpus (3)

• New Approach to Arakelov Geometry
• Les variétés sur le corps à un élément
• Remarks on zeta functions and K-theory over F1

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• Sheaves and $K$-theory for ${\mathbb{F}}_1$-schemes
• Representations of Quivers over F1
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