### Homotopy Theory Seminar

Thursday, December 1, 2022 - 3:30pm

#### Guchuan Li

University of Michigan

Location

University of Pennsylvania

https://upenn.zoom.us/j/91388704495

The group of all invertible objects in a symmetric monoidal category is known as the Picard group. From the chromatic perspective, $K(n)$-local categories are the building blocks of the stable homotopy theory. Hopkins-Mahowald-Sadofsky computed the Picard group of the $K(1)$-local category, which already contains interesting objects. In a joint work in progress with Ningchuan Zhang, we revisit the computation of the Picard group of $K(1)$-local category and upgrade it with a $\mathbb{Z}_p^\times$-equivariant structure.