## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** Brauer groups of commutative ring spectra

**Speaker:** David Gepner

**Speaker Info:**

**Brief Description:**

**Special Note**:

**Abstract:**

The space of units GL_1(R) of a commutative ring spectrum R
is the infinite loop space of a spectrum gl_1(R). Typically, this
spectrum is taken to be connective, meaning it has no nonzero negative
homotopy groups. However, there are other interesting deloopings of
GL_1(R) which carry important algebraic information about R. One in
particular has \pi_{-1} gl_1(R) = \pi_0 Pic(R), the Picard group of R,
and \pi_{-2} gl_1(R) = \pi_0 Br(R), the Brauer group of R. If R is
connective, there is a spectral sequence for computing the homotopy
groups of Pic(R) and Br(R) in terms of the homotopy groups of R and
the etale cohomology of the multiplicative group on Spec \pi_0 R. If S
is a G-Galois extension of R, one obtains a Galois descent spectral
sequence which calculates the Picard and Brauer groups of R relative
to S.

**Date:** Monday, January 09, 2012

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. Paul Goerss

**Contact email:** pgoerss@math.northwestern.edu

**Contact Phone:** 847-491-8544

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