Vladimir Dokchitser and Alexandros Konstantinou

Isogenies between Jacobians

This talk concerns the arithmetic of curves that admit a finite group of automorphisms. We will present a way of constructing isogenies between products of Jacobians of curves using only basic Galois theory and representation theory of finite groups. Our motivation comes from the study of ranks of Jacobians and predictions of the Birch-Swinnerton-Dyer conjecture; however, this discussion will be postponed to the Motivic pieces of curves talk. This is joint work with Holly Green and Adam Morgan.