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.


closed as off topic by David Roberts, Zev Chonoles May 15 '12 at 0:50

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  • 3
    $\begingroup$ This seems like it would be a better question for MO. $\endgroup$ – user21725 May 11 '12 at 5:43
  • $\begingroup$ Heh, I was thinking that it wasn't good enough for MO, but if people agree I can try there. $\endgroup$ – David Roberts May 11 '12 at 7:29
  • $\begingroup$ I agree with Eric. $\endgroup$ – Martin Brandenburg May 14 '12 at 19:00
  • $\begingroup$ Ok. Will close this question. Others please vote to close - I suggest 'off topic' ;-) $\endgroup$ – David Roberts May 15 '12 at 0:38
  • $\begingroup$ @David: I've closed the question. However it'd be good to edit your question to include a link to the MO question once you post it there. $\endgroup$ – Zev Chonoles May 15 '12 at 0:51

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.


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