Is there a semisimple $\mathbf{Q}_\ell$-representation of $G_F$ ramified at an infinite set of places? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T06:14:35Z http://mathoverflow.net/feeds/question/104995 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104995/is-there-a-semisimple-mathbfq-ell-representation-of-g-f-ramified-at-an-in Is there a semisimple $\mathbf{Q}_\ell$-representation of $G_F$ ramified at an infinite set of places? Timo Keller 2012-08-18T18:59:53Z 2012-08-19T22:58:33Z <p>See <a href="http://math.uni.lu/~wiese/galois/Boeckle-Luxemburg-Notes.pdf" rel="nofollow">http://math.uni.lu/~wiese/galois/Boeckle-Luxemburg-Notes.pdf</a>, 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 <em>not finite</em> (for every $\dim{V} \geq 1$)?</p> http://mathoverflow.net/questions/104995/is-there-a-semisimple-mathbfq-ell-representation-of-g-f-ramified-at-an-in/104998#104998 Answer by Timo Keller for Is there a semisimple $\mathbf{Q}_\ell$-representation of $G_F$ ramified at an infinite set of places? Timo Keller 2012-08-18T19:25:42Z 2012-08-18T20:08:28Z <p>It seems that for $\dim{V} = 1$, there is no such representation <a href="http://www.math.leidenuniv.nl/scripties/KretMaster.pdf" rel="nofollow">http://www.math.leidenuniv.nl/scripties/KretMaster.pdf</a> p. 10.</p>