Au-dessous de SpecZ .

@article{Ton2009AudessousDS,
  title={Au-dessous de SpecZ .},
  author={Bertrand To{\"e}n and Michel Vaqui{\'e}},
  journal={Journal of K-theory},
  year={2009},
  volume={3},
  pages={437-500}
}
In this article we use the theories of relative algebraic geometry and of homotopical algebraic geometry (cf. [HAGII]) to construct some categories of schemes defined under Spec ℤ. We define the categories of ℕ-schemes, 1 -schemes, -schemes, + -schemes and 1 -schemes, where (from an intuitive point of view) ℕ is the semi-ring of natural numbers, 1 is the field with one element, is the ring spectra of integers, + is the semi-ring spectra of natural numbers and 1 is the ring spectra with one… 
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