Victor Rotger, "Diagonal cycles and elliptic curves of rank two"

I will describe recent work in collaboration with H. Darmon
and A. Lauder on the construction of an Euler system of diagonal
cycles in the Chow group of suitable fibrations of the product of
three modular curves. According to the conjectures of Beilinson-Bloch,
the behavior of these classes is governed by the L-function associated
by Garrett to the convolution of three cuspidal eigenforms. I will
explain how to deform p-adically these classes in order to shed new
light on the conjecture of Birch&Swinnerton-Dyer in ranks 0, 1 and 2.