Godeaux-Serre varieties and the étale index

We use Godeaux-Serre varieties of finite groups, projective representation theory, the twisted Atiyah-Segal completion theorem, and our previous work on the topological period-index problem to compute the étale index of Brauer classes α Brét(X) in some specific examples. In particular, these computations show that the étale index of α differs from the period of α in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Godeaux-Serre varieties in terms of projective representation theory.