Murphy's Law for gerbes


I will report on joint work with Daniel Bragg. There are many ways to express the universality properties of moduli spaces. For example, Vakil established years ago that any singularity type defined over the integers appears in natural moduli spaces, proving what he called “Murphy’s Law”. We have discovered another, similar, phenomenon: many natural moduli spaces contain all finite gerbes. In particular, any finite gerbe over any field appears as the residual gerbe of some point of the stack of curves.