Resumen de On the surjectivity of the galois representations associated to Non-CM elliptic curves

Alina Carmen Cojocaru

• Let E be an elliptic curve defined over Q, of conductor N and without complex multiplication. For any positive integer l, let phil be the Galois representation associated to the l-division points of E. From a celebrated 1972 result of Serre we know that phil is surjective for any sufficiently large prime l. In this paper we find conditional and unconditional upper bounds in terms of N for the primes l for which phil is not surjective.