On the notion of geometry over $\F_1$

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We refine the notion of variety over the "field with one element" developed by C. Soulé by introducing a grading in the associated functor to the category of sets, and show that this notion becomes compatible with the geometric viewpoint developed by J. Tits. We then solve an open question of C. Soulé by proving, using results of J. Tits and C. Chevalley, that Chevalley group schemes are examples of varieties over a quadratic extension of the above "field".
26 pages

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Algebraic Geometry, Number Theory, Quantum Algebra, 14L15; 11G25; 20G15; 51N30

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http://salesiana.dossiersoluciones.com/handle/123456789/220896

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.2926
 http://arxiv.org/abs/0809.2926

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arXiv