Stacks in arithmetic geometry [closed]

Stacks, of varying kinds, appear in algebraic geometry whenever we have moduli problems, most famously the stacks of (marked) curves. But these seem to be to be very geometric in motivation, so I was wondering if there are natural examples of stacks that arise in arithmetic geometry or number theory.

EDIT: the question is now at MO.

You'd find more arithmetic geometers in MO than here, I reckon. Here's my two cents' worth. There are moduli problems in arithmetic geometry as well, so it's not too surprising that you'd find stacks there as well: in fact, Behrang Noohi has an interesting short article in which he showed how to view the quotient of the upper half plane by the action of a discrete subgroup of $PSL(2,\mathbb{R})$ as a stack (http://www.mth.kcl.ac.uk/~noohi/papers/WhatIsTopSt.pdf). There is also an interesting paper of Henri Gillet, "Arithmetic Intersection Theory on Deligne-Mumford Stacks", that may be of interest.