Serre-Godeaux varieties and the etale index

We use the Serre-Godeaux 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 etale index of Brauer classes alpha in some specific examples. In particular, these computations show that the etale index of alpha differs from the period of alpha in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Serre-Godeaux varieties in terms of projective representation theory.