  In this essay we study various notions of projective space (and other
schemes) over $\mathbb{F}_{1^\ell}$, with $\mathbb{F}_1$ denoting the field
with one element. Our leading motivation is the "Hiden Points Principle," which
shows a huge deviation between the set of rational points as closed points
defined over $\mathbb{F}_{1^\ell}$, and the set of rational points defined as
morphisms $\texttt{Spec}(\mathbb{F}_{1^\ell}) \mapsto \mathcal{X}$. We also
introduce, in the same vein as Kurokawa [13], schemes of
$\mathbb{F}_{1^\ell}$-type, and consider their zeta functions.
