Brauer groups for commutative S-algebras |
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| Authors: | Andrew Baker Birgit Richter Markus Szymik |
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| Affiliation: | 1. School of Mathematics & Statistics, University of Glasgow, Glasgow G12 8QW, Scotland, United Kingdom;2. Fachbereich Mathematik der Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany;3. Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany |
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| Abstract: | We investigate a notion of Azumaya algebras in the context of structured ring spectra and give a definition of Brauer groups. We investigate their Galois theoretic properties, and discuss examples of Azumaya algebras arising from Galois descent and cyclic algebras. We construct examples that are related to topological Hochschild cohomology of group ring spectra and we present a -local variant of the notion of Brauer groups. |
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