Categorical local Langlands for $\mathrm{GL}_n$ for parameters of Langlands-Shahidi type with integral coefficients
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913784670453760 |
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| author | Zou, Konrad |
| author_facet | Zou, Konrad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical local Langlands for $\mathrm{GL}_n$ for parameters of Langlands-Shahidi type with integral coefficients Zou, Konrad Representation Theory Number Theory 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. |
| title | Categorical local Langlands for $\mathrm{GL}_n$ for parameters of Langlands-Shahidi type with integral coefficients |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2504.06499 |