Wojciech J. Gajda

Abstract: Let K be a number field. The Mordell-Weil theorem asserts that the torsion subgroup of the group of K-rational points of any abelian variety A/K is finite. In this talk we will try to understand what is the optimal bound for this group in function of the degree of K over the rationals Q. I will first explain the very concrete case of elliptic curves, then give some explainations on how to compute the optimal bound for a product of elliptic curves and finally I will move to the case of abelian variety of GL_2-type which have a strong similarity with the case of a product of elliptic curves. This is a joint work with M. Hindry.