Murphy's Law for the stack of curves

Abstract: When trying to classify curves over a non-algebraically closed field, one quickly runs into the difficulty that there are curves which are not defined over their fields of moduli. We will explain what this means with some examples. We will discuss how this phenomenon can be thought of geometrically in the moduli space of curves, using residual gerbes. We will then explain some recent work with Max Lieblich on solving the corresponding inverse problem: specifically, we show that every Deligne-Mumford gerbe over a field occurs as the residual gerbe of a point of the moduli stack of curves. This means that every possible way that a curve could fail to be defined over its field of moduli actually does occur, that is, everything that could go wrong does.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca