Ciaran Schembri : Torsion and moduli of surfaces with quaternionic multiplication

Posted by Frederick Saia , part of the Number Theory Seminar.

At

April 26, 2024, 1 p.m.

In

1227 SEO

Abstract

In a celebrated work Mazur classified which torsion subgroups can occur for elliptic curves defined over the rationals. A natural analogue is to consider surfaces with geometric endomorphisms by a quaternion order (PQM surfaces), since the associated moduli space is 1-dimensional. In this talk I will discuss progress towards classifying which torsion subgroups are possible for these surfaces. We also give a description of the moduli problem for PQM surfaces. This is joint work with Eran Assaf, Jef Laga, Freddy Saia, Ari Shnidman, Jacob Swenberg and John Voight.