The diagonal cycle Euler system for ${\rm GL}_2\times{\rm GL}_2$

Raúl Alonso; Francesc Castella; Óscar Rivero

paper

The diagonal cycle Euler system for $GL_{2} \times GL_{2}$

arXiv:2106.05322

Abstract

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 ranks zero and one, and a divisibility towards an Iwasawa main conjecture.

arXiv commentRevised version. To appear in J. Inst. Math. Jussieu

The diagonal cycle Euler system for GL2​×GL2​

Abstract

The diagonal cycle Euler system for $GL_{2} \times GL_{2}$