On depth-zero integral models of local Shimura varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911103222546432 |
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| author | Takaya, Yuta |
| author_facet | Takaya, Yuta |
| contents | We construct integral models and special affinoids of suitable tubular neighborhoods of local Shimura varieties at depth-zero. We show that the reductions of the special affinoids over suitable tamely ramified extensions are realized as parabolic Deligne-Lusztig varieties and explicitly compute part of the middle $\ell$-adic étale cohomology of local Shimura varieties at depth-zero. In the case of general linear groups, our construction recovers generalized semistable models of Lubin-Tate spaces at depth-zero constructed by Yoshida. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On depth-zero integral models of local Shimura varieties Takaya, Yuta Number Theory Algebraic Geometry Representation Theory We construct integral models and special affinoids of suitable tubular neighborhoods of local Shimura varieties at depth-zero. We show that the reductions of the special affinoids over suitable tamely ramified extensions are realized as parabolic Deligne-Lusztig varieties and explicitly compute part of the middle $\ell$-adic étale cohomology of local Shimura varieties at depth-zero. In the case of general linear groups, our construction recovers generalized semistable models of Lubin-Tate spaces at depth-zero constructed by Yoshida. |
| title | On depth-zero integral models of local Shimura varieties |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2505.10000 |