English

Brauer groups for commutative $S$-algebras

Algebraic Topology 2015-08-20 v3 Algebraic Geometry Rings and Algebras

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

Keywords

Cite

@article{arxiv.1005.5370,
  title  = {Brauer groups for commutative $S$-algebras},
  author = {Andrew Baker and Birgit Richter and Markus Szymik},
  journal= {arXiv preprint arXiv:1005.5370},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-21T15:29:19.948Z