Categorical local Langlands for $\mathrm{GL}_n$ for parameters of Langlands-Shahidi type with integral coefficients
Representation Theory
2025-04-10 v1 Number Theory
Abstract
We prove the categorical form of Fargues' geometrization conjecture for along -parameters of Langlands-Shahidi type for rational, torsion, and integral coefficients. Additionally, we prove that in this case the categorical equivalence is -exact, which yields new torsion vanishing results in the cohomology of unitary Shimura varieties.
Cite
@article{arxiv.2504.06499,
title = {Categorical local Langlands for $\mathrm{GL}_n$ for parameters of Langlands-Shahidi type with integral coefficients},
author = {Konrad Zou},
journal= {arXiv preprint arXiv:2504.06499},
year = {2025}
}