%0 Journal Article
%T The Saito–Kurokawa lifting and Darmon points
%+ Institut de Mathématiques de Marseille (I2M)
%+ Dipartimento di Matematica [padova]
%A Nicole, Marc-Hubert
%A Longo, Matteo
%< avec comité de lecture
%@ 0025-5831
%J Mathematische Annalen
%I Springer Verlag
%V 356
%N 2
%P 469-486
%8 2013
%D 2013
%R 10.1007/s00208-012-0846-5
%K Saito-Kurokawa lifting
%K Siegel modular forms
%K Hida family
%K Darmon points
%Z 11F30 11F32 11F46 11F85
%Z Mathematics [math]Journal articles
%X Let E/ℚ be an elliptic curve of conductor Np with p∤N and let f be its associated newform of weight 2. Denote by f∞ the p-adic Hida family passing though f, and by F∞ its Λ-adic Saito–Kurokawa lift. The p-adic family F∞ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients {A˜T(k)}T indexed by positive definite symmetric half-integral matrices T of size 2×2. We relate explicitly certain global points on E (coming from the theory of Darmon points) with the values of these Fourier coefficients and of their p-adic derivatives, evaluated at weight k=2.
%G English
%L hal-01265176
%U https://hal.science/hal-01265176
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-