# nLab Brauer ∞-group

Contents

### Context

#### Higher algebra

higher algebra

universal algebra

group theory

# Contents

## Idea

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

## Properties

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

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

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

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

$\Omega^2 Br(E) \simeq \Omega Pic(E) \simeq GL_1(E) \,.$

## References

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