2015/09/09 by Francesc Castella, Castella, Francesc
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1509.02761
openalex publication_date 2015/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a new proof of Howard's Λ-adic Gross-Zagier formula, which we extend to the context of indefinite Shimura curves over Q attached to nonsplit quaternion algebras. This formula relates the cyclotomic derivative of a two-variable p-adic L-function restricted to the anticyclotomic line to the cyclotomic p-adic heights of Heegner points over the anticyclotomic tower, and our proof, rather than inspired by the original approaches of Gross-Zagier and Perrin-Riou, is via Iwasawa theory, based on the connection between Heegner points, Beilinson-Flach elements, and their explicit reciprocity laws.