|Location:||MSRI: Simons Auditorium|
The group of invertible objects in a symmetric monoidal category is a basic invariant of the category. The Picard group of the category of spectra is known to consist only of the sphere spectrum and its suspensions. In chromatic homotopy theory we consider the categories of spectra localized with respect to the Morava K-theories K(n) (where we first fix a prime p), and these have much richer Picard groups. I will first describe some classical results about these groups. Then I will talk about current work on understanding the Picard group of the K(2)-local category at p=2. This is based on joint
work with Beaudry, Goerss and Henn.