2022/02/25 by V. Hernández, Hernández, Víctor, Santiago Molina +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2202.12573
openalex publication_date 2022/02/25 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/01
Plectic points were introduced by Fornea and Gehrmann as certain tensor products of local pointson elliptic curves over arbitrary number fields F. In rank r≤ [F:ℚ]-situations, they conjecturally come from p-adic regulators of basis of the Mordell-Weil group defined over dihedral extensions of F. In this article we define two variable anticyclotomic p-adic L-functions attached to a family of overconvergent modular symbols defined over F and a quadratic extension K/F. Their restriction to the weight space provide Hida-Rankin p-adic L-functions. If such a family passes through an overconvergent modular symbol attached to a modular elliptic curve E/F, we obtain a p-adic Gross-Zagier formula that computes higher derivatives of such Hida-Rankin p-adic L-functions in terms of plectic points. This result generalizes that of Bertolini and Darmon, which has been key to demonstrating the rationality of Darmon points.