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Categorical local Langlands for $\mathrm{GL}_n$ for parameters of Langlands-Shahidi type with integral coefficients

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arxiv 2504.06499 v1 pith:HSVRM3PR submitted 2025-04-09 math.RT math.NT

Konrad Zou This is my paper · ORCID
classification math.RTmath.NT
keywords categoricalcoefficientsintegrallanglands-shahidimathrmparametersprovetorsion
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abstract

We prove the categorical form of Fargues' geometrization conjecture for $\mathrm{GL}_n$ along $L$-parameters of Langlands-Shahidi type for rational, torsion, and integral coefficients. Additionally, we prove that in this case the categorical equivalence is $t$-exact, which yields new torsion vanishing results in the cohomology of unitary Shimura varieties.

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  1. Categorical local Langlands and torsion classes of some Shimura varieties

    math.NT 2025-05 conditional novelty 6.0 of 10

    For GL_n over unramified p-adic fields, the paper proves the strongly generic part of the categorical local Langlands conjecture with F_l coefficients and derives Harris-Viehmann type identities and torsion vanishing ...

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