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math.AG2008★ 11 cited
On the notion of geometry over $\F_1$
Alain Connes, Caterina Consani
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 th…
math.AG2008
Fun with $\F_1$
Alain Connes, Caterina Consani, Matilde Marcolli
We show that the algebra and the endomotive of the quantum statistical mechanical system of Bost--Connes naturally arises by extension of scalars from the "field with one element"…