Matteo Longo: Half weight modular forms and rational points on elliptic curves

Let E be an elliptic curve, defined over the field of rational numbers, of conductor Np, where N is a positive 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. One can lift each classical form in the Hida family to a half-weight modular forms, by means of a generalized Kohnen-Shintani correspondence (Baruch-Mao). The resulting Fourier coefficients can be p-adically interpolated by rigid analytic functions defined over the weight space. Extending a previous work by Darmon-Tornaria, I will propose a relation between the coefficients of this formal series and certain global points on the elliptic curve E. This is a work in progress with Zhengyu Mao.

The lecture was held within the framework of the Junior Hausdorff Trimester
Program Algebraic Geometry. (4.2.2014)