Ciaran Schembri

Torsion points on abelian surfaces with potential quaternionic multiplication

In a celebrated work Mazur classified which torsion subgroups can occur for elliptic curves defined over the rationals. In this talk I will give an overview to the analogue question of which torsion subgroups can occur for abelian surfaces defined over the rationals which over some extension obtain endomorphisms by an order in a quaternion algebra.