Anticyclotomic diagonal classes and Beilinson--Flach elements
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916942513700864 |
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| author | Alonso, Raúl Omil-Pazos, Lois Rivero, Óscar |
| author_facet | Alonso, Raúl Omil-Pazos, Lois Rivero, Óscar |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anticyclotomic diagonal classes and Beilinson--Flach elements Alonso, Raúl Omil-Pazos, Lois Rivero, Óscar Number Theory 11R23, 11F85 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. |
| title | Anticyclotomic diagonal classes and Beilinson--Flach elements |
| topic | Number Theory 11R23, 11F85 |
| url | https://arxiv.org/abs/2509.07564 |