# Field of definition of a finite etale cover of an anabelian curve

Let $X$ be an anabelian curve over a number field $K$ and let $p:Y\rightarrow X$ be a finite etale cover. Then is anything known (or has anything been conjectured) about the field of definition of $Y$? In particular, should it be an abelian extension of $K$?

-
see the answer to my question, mathoverflow.net/questions/119981/… which implies that you can get really awful extensions this way. –  Will Sawin Feb 25 '13 at 17:06