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Godeaux–Serre varieties and the étale index

Published online by Cambridge University Press:  04 April 2013

Benjamin Antieau  and
Ben Williams
Benjamin Antieau
Affiliation:
UCLA, Department of Mathematics, 520 Portola Plaza, Los Angeles CA 90095-1555, USAantieau@math.ucla.edu
Ben Williams
Affiliation:
USC, Department of Mathematics, 3620 South Vermont Avenue, Los Angeles CA 90089-2532, USAtbwillia@usc.edu
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Abstract

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.

Keywords

Projective representation theoryBrauer groupstwisted K-theoryperiod-index problemsfinite groupsPrimary: 14F2220C25Secondary: 19L50

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Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 2 , April 2013 , pp. 283 - 295
Copyright
Copyright © ISOPP 2013 

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