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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.

flag	asked Jul 1 2010 at 13:48 Ariyan Javanpeykar 4,032●5●28

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This question has a lot of nice answers mathoverflow.net/questions/4075/… – jc Jul 1 2010 at 17:42

David Corfield · Accepted Answer · 2010-07-01 14:07:58Z UTC

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Various pieces of exposition and references are to be found - here, here, here, and here.

answered Jul 1 2010 at 14:07

David Corfield
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This is great. Thanks. – Ariyan Javanpeykar Jul 1 2010 at 15:00

The ring of integers looks like the 3-dimensional sphere viewed as the Hopf fibration

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