# 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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