Title: Picard groups in chromatic homotopy theory
Abstract: Computation of the stable homotopy groups
of spheres is a
long-standing open problem in
algebraic topology. I will describe how
chromatic homotopy theory uses
localization of categories, analogous to
localization of rings and modules, to
split this problem into easier pieces,
called chromatic levels. Each
chromatic level is a symmetric monoidal
category, and we can study their
Picard groups. I will talk about
classical results about these groups,
and about current work on understanding the
Picard group at the
second chromatic level.