  Lichtenbaum conjectured the existence of a Weil-\'etale cohomology in order
to describe the vanishing order and the special value of the Zeta function of
an arithmetic scheme $\mathcal{X}$ at $s=0$ in terms of Euler-Poincar\'e
characteristics. Assuming the (conjectured) finite generation of some \'etale
motivic cohomology groups we construct such a cohomology theory for regular
schemes proper over $\mathrm{Spec}(\mathbb{Z})$. In particular, we obtain
(unconditionally) the right Weil-\'etale cohomology for geometrically cellular
schemes over number rings. We state a conjecture expressing the vanishing order
and the special value up to sign of the Zeta function $\zeta(\mathcal{X},s)$ at
$s=0$ in terms of a perfect complex of abelian groups
$R\Gamma_{W,c}(\mathcal{X},\mathbb{Z})$. Then we relate this conjecture to
Soul\'e's conjecture and to the Tamagawa number conjecture of Bloch-Kato, and
deduce its validity in simple cases.
