SFU Number Theory and Algebraic Geometry Seminar: Daniel Bragg

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.