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The 3-adic Steinberg block and a categorical 3-adic local Langlands correspondence for GL2(ℚ3)
Abstract
We extend the work of Johansson-Newton-Wang-Erickson on a categorical p-adic Langlands correspondence over GL2(ℚp) 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 GL2(ℚ3), obtaining results complementing those of Paškūnas.
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BibTeX
@misc{dowd20263adic,
title = {{The 3-adic Steinberg block and a categorical 3-adic local Langlands correspondence for $\textGL_2(\mathbbQ_3)$}},
author = {CJ Dowd},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25055},
eprint = {2610.25055},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25055},
}
RIS
TY - UNPB
TI - The 3-adic Steinberg block and a categorical 3-adic local Langlands correspondence for GL_2(ℚ_3)
AU - CJ Dowd
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25055
UR - https://arxiv.org/abs/2610.25055
AB - We extend the work of Johansson-Newton-Wang-Erickson on a categorical p-adic Langlands correspondence over GL_2(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 GL_2(ℚ_3), obtaining results complementing those of Paškūnas.
ER -