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Godeaux–Serre varieties and the étale index

  • Benjamin Antieau (a1) and Ben Williams (a2)

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.

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Journal of K-Theory
  • ISSN: 1865-2433
  • EISSN: 1865-5394
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