Les variétés sur le corps à un élément
arXiv:math/0304444
Abstract
We propose a definition of varieties over the field with one element. These have extensions of scalars to the ring of integers which are varieties in the usual sense. We show that toric varieties can be defined over the field with one element. We also discuss zeta functions for such objects. We give a motivic interpretation of the image of the J-homomorphism defined by Adams. ~ ~ ~ ~