Take the 2-minute tour ×  I've heard that the étale fundamental
group of the moduli stack of elliptic curves (over $\mathbb{Z}$)
is trivial. Is there an easy proof of that? (Note that there are
plenty of étale covers once one inverts a prime $p$, given by
taking elliptic curves with some form of a level $p^n$
structure.)  More generally, I'd be interested in how it works
out for the stack of cubic curves which are allowed either to be
smooth or to have a nodal singularity.  share|improve this
question I believe the paper `Horizontal divisors on arithmetic
surfaces associated with Belyĭ uniformizations' by Ihara proves
that the fundamental group of $\mathbb{P}^1\setminus
\{0,1,\infty\}_{\mathbb{Z}}$ is trivial. I'm not sure because I
rarely think about fundamental groups of stacks, but the result
you want might follow from this. –  Minhyong Kim Aug 19 '12 at
17:36 Upon further thought, maybe not. –  Minhyong Kim Aug 19
'12 at 17:53 I dunno, that implication sounds reasonable to me!
–  JSE Aug 19 '12 at 20:38