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

• Autores: Alina Carmen Cojocaru
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 1, 2005, págs. 16-31
• Idioma: inglés
• DOI: 10.4153/cmb-2005-002-x
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• Resumen

  • 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.