The 3-adic Steinberg block and a categorical 3-adic local Langlands correspondence for $\text{GL}_2(\mathbb{Q}_3)$
Year: 2026
Type: preprint
Abstract: 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 construction without requiring an explicit algebraic presentation. As input to this argument, we also perform some new analysis of the representation theory of the $3$-adic Steinberg block of $\text{GL}_2(\mathbb{Q}_3)$, obtaining results complementing those of Paškūnas.
Source: arXiv (Cornell University)
Author: Dowd, CJ
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223037177