Abstract: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.
| Comments: | 31 pages of content. Comments are welcome! |
| Subjects: | Number Theory (math.NT) |
| Cite as: | arXiv:2605.24148 [math.NT] |
| (or arXiv:2605.24148v1 [math.NT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24148 arXiv-issued DOI via DataCite (pending registration) |
From: Sandra Nair [view email]
[v1]
Fri, 22 May 2026 19:11:36 UTC (30 KB)
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