The 3-adic Steinberg block and a categorical 3-adic local Langlands correspondence for $\text{GL}_2(\mathbb{Q}_3)$

We extend the work of Johansson-Newton-Wang-Erickson on a categorical $p$-adic Langlands correspondence over $\text{GL}_2(\mathbb{Q}_p)$ to $p = 3$ by recontextualizing their construction in the Steinberg case. We produce a novel, more categorical method of analyzing the properties of this construct