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.
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