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.



The ring of integers  looks  like the 3-dimensional sphere viewed as the Hopf fibration
Various pieces of exposition and references are to be found - [here](http://golem.ph.utexas.edu/category/2007/10/this_weeks_finds_in_mathematic_18.html), [here](http://math.ucr.edu/home/baez/week257.html), [here](http://www.ucl.ac.uk/~ucahmki/baez13.12.pdf), and [here](http://golem.ph.utexas.edu/category/2009/04/afternoon_fishing.html).


