Anticyclotomic diagonal classes and Beilinson–Flach elements
Raúl Alonso, Lois Omil-Pazos, Óscar Rivero
Source abstract
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 -adic -functions and Perrin–Riou maps and exploits the Eisenstein degeneration of diagonal cycles along Hida families, working with a CM family that specializes to an irregular Eisenstein series in weight one. We use these results to derive some arithmetic applications.
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