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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 $\dim{V} \geq 1$)?

Edit: It seems that for $\dim{V} = 1$, there is no such representation.

3 fix title "unramified" -> "ramified"

# Is there a semisimple $\mathbf{Q}_\ell$-representation of $G_F$ unramifiedramified at an infinite set of places?

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