On the notion of geometry over 𝔽₁-Reference-Cited by-同舟云学术

On the notion of geometry over 𝔽₁

Published:2010-12-08 Issue:3 Volume:20 Page:525-557
ISSN:1056-3911
Container-title:Journal of Algebraic Geometry
language:en
Short-container-title:J. Algebraic Geom.

Author:

Connes Alain,Consani Caterina

Abstract

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”.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology,Algebra and Number Theory

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