On the notion of geometry over $\F_1$

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dc.creatorConnes, Alain
dc.creatorConsani, Caterina
dc.date2008-09-17
dc.date2009-02-22
dc.date.accessioned2026-07-07T12:44:48Z
dc.date.available2026-07-07T12:44:48Z
dc.descriptionWe 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".
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/0809.2926
dc.identifierhttp://arxiv.org/abs/0809.2926
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220896
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subjectQuantum Algebra
dc.subject14L15; 11G25; 20G15; 51N30
dc.titleOn the notion of geometry over $\F_1$
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