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arXiv · 2509.07564

Anticyclotomic diagonal classes and Beilinson--Flach elements

Raúl Alonso·Lois Omil-Pazos·Óscar Rivero
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Abstract

We present a comparison between the anticyclotomic Euler system of diagonal cycles associated with the convolution of two modular forms and the cyclotomic Beilinson--Flach Euler system. This extends the seminal work of Bertolini, Darmon, and Venerucci, who established a link between (anticyclotomic) Heegner points and the Beilinson--Kato system. Our approach hinges on a detailed analysis of $p$-adic $L$-functions and Perrin-Riou maps and exploits the Eisenstein degeneration of diagonal cycles along Hida families, working with a CM family which specializes to an irregular Eisenstein series in weight one. We use these results to derive some arithmetic applications.

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Raúl Alonso, Lois Omil-Pazos, Óscar Rivero. 2025-09-09. Anticyclotomic diagonal classes and Beilinson--Flach elements. https://arxiv.org/abs/2509.07564

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