Categorical local Langlands and torsion classes of some Shimura varieties
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915289681100800 |
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| author | Nguyen, Kieu Hieu |
| author_facet | Nguyen, Kieu Hieu |
| contents | We study the cohomology of various local Shimura varieties for $GL_n$. This provides an explicit description of the spectral action constructed by Fargues-Scholze in certain cases and allows us to prove some strongly generic part of the categorical local Langlands conjecture for $GL_n$ with torsion coefficients. As applications, we are able to prove an analogue of the Harris-Viehmann conjecture and deduce new vanishing results for the cohomology of Shimura varieties of type A in the torsion coefficient setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10724 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical local Langlands and torsion classes of some Shimura varieties Nguyen, Kieu Hieu Number Theory Algebraic Geometry Representation Theory We study the cohomology of various local Shimura varieties for $GL_n$. This provides an explicit description of the spectral action constructed by Fargues-Scholze in certain cases and allows us to prove some strongly generic part of the categorical local Langlands conjecture for $GL_n$ with torsion coefficients. As applications, we are able to prove an analogue of the Harris-Viehmann conjecture and deduce new vanishing results for the cohomology of Shimura varieties of type A in the torsion coefficient setting. |
| title | Categorical local Langlands and torsion classes of some Shimura varieties |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2505.10724 |