| Résume | Let $E$ be an elliptic curve, defined over the field of rational numbers, of arithmetic conductor $Np$, where $N>1$ is an integer and $p$ is a prime which does not divide $N$. Let $f$ be the weight 2 newform attached to $E$. We consider the Hida family passing through $f$. To each classical form in the Hida family, we may associate its Saito-Kurokawa lifting. It is known that there exists a p-adic family of Siegel modular forms interpolating these liftings, in the same way as the original Hida family interpolates classical forms. The family of Siegel modular forms can be written as an explicit formal power series expansion. We show a relation beteen the coefficients of this formal series and certain global points on the elliptic curve E. The global points have been introduced by H. Darmon in 2001, explaining the title of the talk. This is a joint work with M.-H. Nicole. |
