Anticyclotomic Euler systems and diagonal cycles

Abstract: In this talk, I will discuss joint work with Raul Alonso and Francesc Castella where we construct an anticyclotomic Euler system for the Rankin$-$Selberg convolutions of two modular forms, using $p$-adic families of generalized Gross$-$Kudla$-$Schoen diagonal cycles. As applications of this construction, we prove new cases of the Bloch$-$Kato conjecture in analytic rank zero (and results towards new cases in analytic rank one), and a divisibility towards an Iwasawa main conjecture. If time permits, I will also consider the case of the symmetric square of a modular form, where the key ingredient is a factorization formula for the triple product $p$-adic $L$-function.

algebraic geometrynumber theory

Audience: researchers in the topic

Number Theory Seminars at Università degli Studi di Padova