Brauer groups of moduli of hyperelliptic curves via cohomological invariants

Abstract

We compute the Brauer group of the moduli stack of hyperelliptic curves ${\mathcal{H}}_g$ over any field of characteristic zero. In positive characteristic, we compute the part of the Brauer group whose order is prime to the characteristic of the base field.

35 pages, comments are very welcome! New version: we extended our choice of coefficients to general cycle modules, using Gille and Hirsch's results (arXiv:1908.08146). Our methods moreover yield a more precise descriptions of the groups appearing in Gille and Hirsch's splitting formula