On the Surjectivity of Galois Representations Associated to Elliptic Curves over Number Fields

Eric Larson, Dmitry Vaintrob

Given an elliptic curve $E$ over a number field $K$, the $\ell$-torsion points $E[\ell ]$ of $E$ define a Galois representation $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$. A famous theor…