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replaced http://mathoverflow.net/ with https://mathoverflow.net/

edited Apr 13, 2017 at 12:58

There are several MO-hard problems about smooth and proper schemes over $\mathbb Z$, including:

Smooth proper schemes over $\mathbb Z$ with points everywhere locally

Non-simply-connected smooth proper scheme over $\mathbb Z$

What can be the dimension of a pointless smooth proper $\mathbb Z$-scheme?

All these were inspired by Poonen's (solved) question, asking whether such a scheme necessarily has a section:

Smooth proper scheme over $\mathbb Z$

answered Aug 27, 2014 at 0:42