This question is based on the following phrase:

"In a sense, $\textrm{Spec} \ \mathbf{Z}$ looks topologically like a 3-dimensional sphere viewed as the Hopf fibration over $\mathbf{S}^2$."

See page 88 of *Algebraic Geometry II* by Shafarevich.

I find this remark very interesting but I can't seem to parse it.

I always just viewed $\textrm{Spec} \ \mathbf{Z}$ as an arithmetic analogue of $\mathbf{P}^1(\mathbf{C}) = \mathbf{S}^2$. This remark would add "something" to that in a sense.