During this semester will study Galois representations attached to elliptic curves without complex multiplication defined over number fields. In particular, we will use Oguz's master thesis as a guide to understand Serre's theorem on the surjectivity of certain respresentations.
References:
C. O. Oguz, Galois Representations Attached to Elliptic curves. Master Thesis, University of Bordeaux 1 (2012).
J-P. Serre, “Les propriétés galoisiennes des points des torsions des courbes elliptiques,” Inventiones mathematicae, vol. 15, pp. 259–331, 1972.
J. Silverman; J. Tate, Rational Points on Elliptic Curves. Springer International Publishing (2015).
J. Silverman, The Arithmetic of Elliptic Curves, vol. 106. Springer-Verlag, New York (2009).