You are cordially invited to the Arithmetic Geometry & Number Theory Seminar organized by the Department of Mathematics.
Speaker: Rose Lopez (Bilkent University)
“Shimura Curves as stacks and Atkin-Lehner involutions on them”
Abstract: I will be presenting on work in progress joint with John Voight towards understanding Shimura curves as stacks. Shimura curves are a generalization of modular curves which classify principally polarized abelian surfaces with quaternionic multiplication (QM). We study the forgetful map from the Shimura curve to A2, the moduli stack of principally polarized abelian surfaces, as well as the quotient of the Shimura curve by the action of the Atkin–Lehner group, which acts by permuting the QM structures.
For the Shimura curve attached to the quaternion algebra of discriminant 6, Baba Granath shows that at the level of schemes, the Atkin–Lehner quotient of the Shimura curve is isomorphic to the image of the Shimura curve under the forgetful map. However, an analysis of stabilizer groups implies that this is not an isomorphism at the level of stacks. I will explain our theorem-in-progress that at the level of stacks, this map is a normalization
Date: Tuesday, October 20, 2026
Time: 14:00-15:00
Place: SA-240