Number Theory Seminar

Speaker: Fernando Trejos Suarez (Princeton) Title: Euler Systems and Bloch--Kato for the Triple Product Abstract: We discuss the construction of an Euler system for the triple product, the p-adic Galois representation V = V_1 x V_2 x V_3, where V_1,V_2,V_3 are the 2-dimensional representations attached to cuspforms f_1,f_2,f_3. Applications include new cases of the Bloch—Kato conjecture: e.g. in the case that f_i is an elliptic curve E_i over the rationals, and if χ denotes a non-trivial Dirichlet character, we prove (under some technical assumptions) that the non-vanishing of L(E_1 x E_2 x E_3 x χ, s) at the central value s=2 implies the vanishing of the relevant Selmer group for V(χ). The construction is geometric, taking place on the Shimura variety for GSp(4), and uses the pullback method pioneered by Sangiovanni—Skinner. (This talk will not assume any prior knowledge of Euler systems.)