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arXiv · 2106.05322

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

Raúl Alonso·Francesc Castella·Óscar Rivero
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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.

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Raúl Alonso, Francesc Castella, Óscar Rivero. 2021-06-09. The diagonal cycle Euler system for ${\rm GL}_2\times{\rm GL}_2$. https://arxiv.org/abs/2106.05322

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