Brauer groups for commutative $S$-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.

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

References in corpus (7)

• Topological Hochschild homology and cohomology of A_\infty ring spectra
• Brauer groups and étale cohomology in derived algebraic geometry
• String topology and the based loop space
• Brauer groups and Galois cohomology of commutative ring spectra
• A modular description of the K(2)-local sphere at the prime 3
• Azumaya Objects in Triangulated Bicategories
• Iterated homotopy fixed points for the Lubin-Tate spectrum, with an Appendix: An example of a discrete G-spectrum that is not hyperfibrant

Cited by in corpus (8)

• Brauer groups and étale cohomology in derived algebraic geometry
• The higher Morita category of $E_n$-algebras
• Brauer groups and Galois cohomology of commutative ring spectra
• Azumaya Objects in Triangulated Bicategories
• Derived Azumaya algebras and generators for twisted derived categories
• Adjoining roots in homotopy theory
• Homotopy fixed points for profinite groups emulate homotopy fixed points for discrete groups
• The relative Brauer group of $K(1)$-local spectra