For smooth algebraic varieties $X$ over $\mathbb{C}$, the Riemann existence theorem establishes an equivalence of categories between the category of finite etale covers of $X$ and finite unramified covers of $X^\text{an}$.


If $X$ is instead a Deligne Mumford stack over Spec $\mathbb{C}$ corresponding to a complex orbifold $X^\text{an}$, is there an analogous theorem providing an equivalence between finite etale morphisms from DM stacks to $X$ and finite orbifold coverings of $X^\text{an}$? (hence etale fundamental group of such a DM stack is just the profinite completion of the orbifold fundamental group?)


In particular, I'm thinking of the situation where the stack is the moduli stack of elliptic curves over $\mathbb{C}$ and the orbifold is just $\mathcal{H}/SL\_2(\mathbb{Z})$.


Can anyone provide a reference to a precise statement?



Is there a Riemann existence theorem for orbifolds?
The answer is yes. See Theorem 20.4 on p. 80 in Behrang Noohi's 


<http://arxiv.org/pdf/math/0503247v1.pdf>


