On the Harris-Viehmann conjecture for Hodge-Newton reducible local Shimura data of abelian type
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918532153868288 |
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| author | Nair, Sandra Zhou, Xinyu |
| author_facet | Nair, Sandra Zhou, Xinyu |
| contents | We address a new case of the Harris-Viehmann conjecture, which establishes a parabolic induction formula on the cohomology groups associated to non-basic local Shimura data. It follows that all supercuspidal representations on a Shimura variety are concentrated along the basic locus, making the conjecture relevant to the Langlands program. Historically, many cases of the Harris-Viehmann conjecture have been approached with the additional condition of Hodge-Newton reducibility on the underlying local Shimura datum. Building on previous work by Mantovan (EL/PEL case) and Hong (Hodge case), we extend the proof of the conjecture to unramified non-basic local Shimura data of abelian type under the assumption of Hodge-Newton reducibility. We leverage Shen's construction of Rapoport-Zink spaces of abelian type at the hyperspecial level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24148 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Harris-Viehmann conjecture for Hodge-Newton reducible local Shimura data of abelian type Nair, Sandra Zhou, Xinyu Number Theory We address a new case of the Harris-Viehmann conjecture, which establishes a parabolic induction formula on the cohomology groups associated to non-basic local Shimura data. It follows that all supercuspidal representations on a Shimura variety are concentrated along the basic locus, making the conjecture relevant to the Langlands program. Historically, many cases of the Harris-Viehmann conjecture have been approached with the additional condition of Hodge-Newton reducibility on the underlying local Shimura datum. Building on previous work by Mantovan (EL/PEL case) and Hong (Hodge case), we extend the proof of the conjecture to unramified non-basic local Shimura data of abelian type under the assumption of Hodge-Newton reducibility. We leverage Shen's construction of Rapoport-Zink spaces of abelian type at the hyperspecial level. |
| title | On the Harris-Viehmann conjecture for Hodge-Newton reducible local Shimura data of abelian type |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.24148 |