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

2010-07-01T13:48:46Z

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.

Answer by David Corfield for The ring of integers looks like the 3-dimensional sphere viewed as the Hopf fibration

2010-07-01T14:07:58Z

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

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

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

Answer by David Corfield for The ring of integers looks like the 3-dimensional sphere viewed as the Hopf fibration