English

Les vari\'et\'es sur le corps \`a un \'el\'ement

Algebraic Geometry 2007-05-23 v1 Number Theory

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. ~ ~ ~ ~

Keywords

Cite

@article{arxiv.math/0304444,
  title  = {Les vari\'et\'es sur le corps \`a un \'el\'ement},
  author = {Christophe Soulé},
  journal= {arXiv preprint arXiv:math/0304444},
  year   = {2007}
}
R2 v1 2026-07-22T16:54:01.810Z