Tuesday, 30 October 2007

ag.algebraic geometry - The ring of integers looks like the 3-dimensional sphere viewed as the Hopf fibration

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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