### Source

This question came up in the discussion between [Kevin Buzzard](http://mathoverflow.net/users/1384/kevin-buzzard) and [Minhyong Kim](http://mathoverflow.net/users/1826/minhyong-kim) in the comments to [Smooth proper scheme over Z](http://mathoverflow.net/questions/9576/smooth-proper-scheme-over-z/9605#9605). It's a nice one, so I took the liberty of posting it as a community wiki.

### Question

> Is there an example of smooth proper variety $X \to \mathop{\text{Spec}}\mathbb Z$ such that $\pi_1(X) \ne 0$?

### About tags
We recently had other questions of the form "Example of ... with everywhere good reduction at $\mathbb Z$" ([local-global](http://mathoverflow.net/questions/10569/smooth-proper-schemes-over-z-with-points-everywhere-locally), [abelian varieties](http://mathoverflow.net/questions/10860/why-no-abelian-varieties-over-z)). I think it would be interesting to create a tag to group these. Thoughts?