Refined singular moduli through p-adic Galois deformationsMPIM

by Michael Daas (University of Leiden/MPIM)

Tuesday Jun 2, 2026, 2:00 PM → 3:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

In the 1980s, Gross and Zagier studied the norms of the differences between singular moduli.
Analogous questions on Shimura curves allow for purely p-adic investigations through their p-adic uniformisations.
In earlier work, infinitesimal deformations of Galois representations were used to compute the norms of the differences between these singular moduli without relying on their connection to geometry.
We explain how more intricate deformations can be used to obtain results beyond the norm, supporting purely p-adic methods to prove the algebraicity of conjecturally algebraic p-adic quantities.
This is joint work in progress with Yingkun Li.