See <http://math.uni.lu/~wiese/galois/Boeckle-Luxemburg-Notes.pdf>, Theorem 1.4(a): Is there an example of a semisimple $\mathbf{Q}\_\ell$-representation $V$ of $G\_F$ ($F$ a global field) ramified at a set $S$ of places where $S$ is *not finite* (for every $\dim{V} \geq 1$)?



Is there a semisimple $\mathbf{Q}_\ell$-representation of $G_F$ ramified at an infinite set of places?
It seems that for $\dim{V} = 1$, there is no such representation <http://www.math.leidenuniv.nl/scripties/KretMaster.pdf> p. 10.


