Wojciech J. Gajda

Abstract:

Recall that the Galois action on the torsion points of an abelian variety gives rise to an adelic representation of the absolute Galois group. For many classes of abelian varieties there are some limitations on the size of the image of this representation. During the talk we discuss the case of a product of hyperelliptic Jacobians. We give a simple criterion that assures that this representation has maximal Galois image in a certain sense. As an application, we provide a method of constructing products of Jacobians with division fields (i.e. fields obtained by adjoining the coordinates of the torsion points) as disjoint as they can be.