| Abstract: | The aim of these lectures is to present through different examples a construction of Euler systems from the study of congruences between modular forms of various level and weights. The first lecture will be devoted to the case of adjoint modular Galois representations for which I will explain the construction of a rank 2 Euler system under a conjectural property of the annihilators of certain congruence modules for abelian base change. The other lectures will be devoted to the case of Eisenstein congruences. I will first show how the GL(2)-case can be settled unconditionally, and then explain how this strategy will be extend also unconditionally to the general symplectic or unitary case in the ordinary setting according to the time and the interests of the audience. |
