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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2505.12488 |
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| _version_ | 1866912381299326976 |
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| author | Micolet, Gabriel |
| author_facet | Micolet, Gabriel |
| contents | Let $F$ be a totally real field, $p$ a prime that we allow to ramify in $F$, and $B$ a quaternion algebra over $F$ which is split at places over $p$. We consider a smooth $p$-adic integral model, the Pappas-Rapoport model, of the Quaternionic Shimura variety attached to $B$ with prime-to-$p$ level, and the Goren-Oort stratification of its characteristic $p$ fiber. Furthermore, we also introduce Pappas-Rapoport models at Iwahori level $p$ along with a stratification of their characteristic $p$ fiber. We prove that these strata are isomorphic to products of $\mathbb{P}^1$-bundles over auxiliary Quaternionic Shimura varieties, from which we deduce the corresponding description of the Goren-Oort strata. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A mod $p$ Geometric Jacquet-Langlands Relation for Quaternionic Shimura Varieties at Ramified Primes Micolet, Gabriel Number Theory Let $F$ be a totally real field, $p$ a prime that we allow to ramify in $F$, and $B$ a quaternion algebra over $F$ which is split at places over $p$. We consider a smooth $p$-adic integral model, the Pappas-Rapoport model, of the Quaternionic Shimura variety attached to $B$ with prime-to-$p$ level, and the Goren-Oort stratification of its characteristic $p$ fiber. Furthermore, we also introduce Pappas-Rapoport models at Iwahori level $p$ along with a stratification of their characteristic $p$ fiber. We prove that these strata are isomorphic to products of $\mathbb{P}^1$-bundles over auxiliary Quaternionic Shimura varieties, from which we deduce the corresponding description of the Goren-Oort strata. |
| title | A mod $p$ Geometric Jacquet-Langlands Relation for Quaternionic Shimura Varieties at Ramified Primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.12488 |