Hyperelliptic curves with quaternion multiplication, and their arithmetic

Wednesday, 14 June 2023

Abstract

For each even genus g, we study explicitly the family of hyperelliptic curves with a specific action by the quaternion group of order 8.  In particular, using an inductive strategy we determine the endomorphism ring of the Jacobians of curves parametrized in this family, and we find along the way rather special properties of the associated Galois representations. This is joint work with Victoria Cantoral-Farfan and Davide Lombardo.