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

TL;DR

This paper proves that the stable Picard group of the algebra (2) is generated by two elements, showing it has no exotic elements, using descent methods in the stable module category.

Contribution

It establishes the structure of the stable Picard group of (2) as free on two generators, with no exotic elements, via descent techniques.

Findings

The stable Picard group of (2) is free on two generators.

There are no exotic elements in this Picard group.

Descent methods effectively analyze the stable category of (2)-modules.

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.