English

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 GLn\mathrm{GL}_n along LL-parameters of Langlands-Shahidi type for rational, torsion, and integral coefficients. Additionally, we prove that in this case the categorical equivalence is tt-exact, which yields new torsion vanishing results in the cohomology of unitary Shimura varieties.

Keywords

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}
}