The stable Picard group of $\mathcal{A}(2)$

Abstract

Using a form of descent in the stable category of $\mathcal{A}(2)$-modules, we show that there are no exotic elements in the stable Picard group of $\mathcal{A}(2)$, \textit{i.e.} that the stable Picard group of $\mathcal{A}(2)$ is free on $2$ generators.