# Tame ramification and families of curves

Suppose I have a stable curve $$C \rightarrow \mathrm{Spec} R$$ over a complete DVR which has smooth generic fiber and regular total space. If I look at $N$-torsion of the Jacobian of the generic fiber, this defines a ramified cover of my base. Are there any geometric conditions I can impose on my curve that will give me control on the ramification? For instance, if the Jacobian extends to a proper group scheme over $R$, then there is no ramification. But more generally?

-
Even if the Jacobian extends to a proper group scheme over $R$, there can be ramification if the characteristic of the residue field divides $N$. –  Jason Starr Feb 24 '12 at 12:23