Number Theory Seminar
Ciaran Schembri
Dartmouth College
Torsion and moduli of surfaces with quaternionic multiplication
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.
Friday April 26, 2024 at 1:00 PM in 1227 SEO