Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 2, pp. 517-525 (2008)

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$\F_1$-schemes and toric varieties

Anton Deitmar

Mathematisches Institut, Auf der Morgenstelle 10, 72076 Tübingen, Germany, e-mail: deitmar@uni-tuebingen.de

Abstract: In this paper it is shown that integral $\F_1$-schemes of finite type are essentially the same as toric varieties. A description of the $\F_1$-zeta function in terms of toric geometry is given. Etale morphisms and universal coverings are introduced.

Keywords: F1-schemes, toric varieties, field of one element

Classification (MSC2000): 14A15, 11G25, 14L32, 14M32

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Electronic version published on: 18 Sep 2008. This page was last modified: 28 Jan 2013.

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