nLab
Brauer ∞-group

Contents

Context

Higher algebra

Group Theory

Contents

Idea

The refinement of the concept of Brauer group from algebra to higher algebra and stable homotopy theory.

Definition

(Szymik 11, def. 3.8, prop. 5.5)

Properties

Relation to Picard \infty-group and \infty-group of units

Given an E-∞ ring EE, the looping of the Brauer \infty-group is the Picard ∞-group (Szymik 11, theorem 5.7).

ΩBr(E)Pic(E). \Omega Br(E) \simeq Pic(E).

The looping of that is the ∞-group of units (Sagave 11, theorem 1.2).

Ω 2Br(E)ΩPic(E)GL 1(E). \Omega^2 Br(E) \simeq \Omega Pic(E) \simeq GL_1(E) \,.

References

Created on April 1, 2014 at 10:41:28. See the history of this page for a list of all contributions to it.