On the generic part of the cohomology of Shimura varieties of abelian type
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911154597527552 |
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| author | Yang, Xiangqian Zhu, Xinwen |
| author_facet | Yang, Xiangqian Zhu, Xinwen |
| contents | This article contributes to the study of the generic part of the cohomology of Shimura varieties. Under a mild restriction of the characteristic of the coefficient field, we prove a torsion vanishing result for Shimura varieties of abelian type, confirming a conjecture by Hamann--Lee. Our proofs utilize the unipotent categorical local Langlands correspondence and, in contrast to previous works, do not rely on the endoscopic classification of representations or on other results established through trace formula techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the generic part of the cohomology of Shimura varieties of abelian type Yang, Xiangqian Zhu, Xinwen Number Theory Algebraic Geometry Representation Theory This article contributes to the study of the generic part of the cohomology of Shimura varieties. Under a mild restriction of the characteristic of the coefficient field, we prove a torsion vanishing result for Shimura varieties of abelian type, confirming a conjecture by Hamann--Lee. Our proofs utilize the unipotent categorical local Langlands correspondence and, in contrast to previous works, do not rely on the endoscopic classification of representations or on other results established through trace formula techniques. |
| title | On the generic part of the cohomology of Shimura varieties of abelian type |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2505.04329 |