A name for primes where residual Galois representations are reducible - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T07:52:23Z http://mathoverflow.net/feeds/question/6980 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/6980/a-name-for-primes-where-residual-galois-representations-are-reducible A name for primes where residual Galois representations are reducible David Hansen 2009-11-27T20:49:10Z 2010-12-13T02:49:55Z <p>Let $\overline{\rho}_{\Delta,\ell}$ be the mod-$\ell$ representation associated to Ramanujan's $\Delta$-function. It is well-known that (the semisimplification of) this representation is reducible if, say, $\ell=5$ or $\ell=691$. Is there a general name for primes like this? Serre calls them (in a more general context) "exceptional primes," but the word exceptional always strikes me as vague. "Primes of residual reducibility"?</p> http://mathoverflow.net/questions/6980/a-name-for-primes-where-residual-galois-representations-are-reducible/6993#6993 Answer by TG for A name for primes where residual Galois representations are reducible TG 2009-11-27T22:10:09Z 2009-11-27T22:10:09Z <p>"Eisenstein" ? </p>