Brauer groups for commutative $S$-algebras

Details Brauer groups for commutative $S$-algebras Brauer groups for commutative $S$-algebras

2010-05-28

arxiv.org/abs/1005.5370v3

Mathematics

Algebraic Topology

Many changes and improvements, including discussion of connections with other recent work

Scientific paper

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 K(n)-local variant of the notion of Brauer groups.

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