Brauer spaces for commutative rings and structured ring spectra

Details Brauer spaces for commutative rings and structured ring spectra Brauer spaces for commutative rings and structured ring spectra

2011-10-13

arxiv.org/abs/1110.2956v1

Mathematics

K-Theory and Homology

24 pages

Scientific paper

Using an analogy between the Brauer groups in algebra and the Whitehead groups in topology, we first use 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. Natural maps relate these in the case of extensions and in the case of Eilenberg-Mac Lane spectra.

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