Guido Lido

Joint work with Bas Edixhoven. We present a generalization of Chabauty's method, that allows to compute the rational points on curves/Q when the Mordell-Weil rank is strictly smaller than g+s-1, where g is th genus of the curve and s is the rank of the Néron-Severi group of the Jacobian. The main actor in this method is the Poincaré torsor of the Jacobian of the curve, and the method ultimately consists in intersecting the integral points on the Poincaré torsor with an image of the Z_p-points on the curve.