Iwasawa theory for ${\rm GL}_2\times{\rm GL}_2$ and diagonal cycles

Raúl Alonso, Francesc Castella, Óscar Rivero

Published 2021-06-09Version 1

We construct an anticyclotomic Euler system for the Rankin--Selberg convolution 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.