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We use the Serre-Godeaux varieties of finite groups, projectiverepresentation theory, the twisted Atiyah-Segal completion theorem, and ourprevious work on the topological period-index problem to compute the etaleindex of Brauer classes alpha in some specific examples. In particular, thesecomputations show that the etale index of alpha differs from the period ofalpha in general. As an application, we compute the index of unramified classesin the function fields of high-dimensional Serre-Godeaux varieties in terms ofprojective representation theory.

Serre-Godeaux varieties and the etale index