Some vanishing results for the rational completed cohomology of Shimura varieties
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912987843919872 |
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| author | Lan, Kai-Wen Pan, Lue |
| author_facet | Lan, Kai-Wen Pan, Lue |
| contents | Based on an almost Kodaira-type vanishing result in mixed characteristics of Bhatt, we show that, in the locally analytic completed cohomology of a general Shimura variety, sufficiently regular infinitesimal weights can only show up in the middle degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some vanishing results for the rational completed cohomology of Shimura varieties Lan, Kai-Wen Pan, Lue Number Theory 11F77, 11G18, 11F33, 14F17, 14F30 Based on an almost Kodaira-type vanishing result in mixed characteristics of Bhatt, we show that, in the locally analytic completed cohomology of a general Shimura variety, sufficiently regular infinitesimal weights can only show up in the middle degree. |
| title | Some vanishing results for the rational completed cohomology of Shimura varieties |
| topic | Number Theory 11F77, 11G18, 11F33, 14F17, 14F30 |
| url | https://arxiv.org/abs/2603.27932 |