Joint PU/IAS Number Theory

In a recent joint work with S. Iyengar, C. Khare and J. Manning, we use their notion of congruence modules in higher codimension to give a new construction of the bottom class of the rank d=[F:\Q] Euler system attached to nearly ordinary Hilbert modular forms for a totally real field F that I constructed a few years ago. In this talk, I will discuss the non ordinary case for elliptic cusp forms and the construction of Zeta elements in the exterior square of the Galois cohomology for adjoint modular Galois representations.