English

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

Number Theory 2023-05-18 v3

Abstract

We construct an anticyclotomic Euler system for the Rankin-Selberg convolution of two modular forms, using pp-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.

Keywords

Cite

@article{arxiv.2106.05322,
  title  = {The diagonal cycle Euler system for ${\rm GL}_2\times{\rm GL}_2$},
  author = {Raúl Alonso and Francesc Castella and Óscar Rivero},
  journal= {arXiv preprint arXiv:2106.05322},
  year   = {2023}
}

Comments

Revised version. To appear in J. Inst. Math. Jussieu

R2 v1 2026-06-24T03:01:43.051Z