English

Brauer spaces for commutative rings and structured ring spectra

K-Theory and Homology 2016-12-30 v2 Algebraic Topology

Abstract

Using an analogy between the Brauer groups in algebra and the Whitehead groups in topology, we first use methods of algebraic K-theory to give a natural definition of Brauer spectra for commutative rings, such that their homotopy groups are given by the Brauer group, the Picard group and the group of units. Then, in the context of structured ring spectra, the same idea leads to two-fold non-connected deloopings of the spectra of units.

Keywords

Cite

@article{arxiv.1110.2956,
  title  = {Brauer spaces for commutative rings and structured ring spectra},
  author = {Markus Szymik},
  journal= {arXiv preprint arXiv:1110.2956},
  year   = {2016}
}

Comments

29 pages; background added and Brauer group is group of components now

R2 v1 2026-06-21T19:19:46.694Z