Unitary Shimura varieties at ramified primes and arithmetic transfer
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909777787879424 |
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| author | Luo, Yu Mihatsch, Andreas Zhang, Zhiyu |
| author_facet | Luo, Yu Mihatsch, Andreas Zhang, Zhiyu |
| contents | We consider unitary Shimura varieties at places where the totally real field ramifies over $\mbQ$. Our first result constructs comparison isomorphisms between absolute and relative local models in this context, which relies on a reformulation of the Eisenstein condition of Rapoport--Zink and Rapoport--Smithling--Zhang. Related to that, we also provide a moduli description for the integral models of RSZ unitary Shimura varieties in new cases. Our second result lifts the comparison of local models to categories of $p$-divisible groups and, as a corollary, to various kinds of Rapoport--Zink spaces. Our third result is a proof of the arithmetic transfer conjecture of the third author in full generality. Using our statements about Rapoport--Zink spaces, we extend the previous proof from the unramified case to that of all $p$-adic local fields ($p$ odd). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unitary Shimura varieties at ramified primes and arithmetic transfer Luo, Yu Mihatsch, Andreas Zhang, Zhiyu Algebraic Geometry Number Theory We consider unitary Shimura varieties at places where the totally real field ramifies over $\mbQ$. Our first result constructs comparison isomorphisms between absolute and relative local models in this context, which relies on a reformulation of the Eisenstein condition of Rapoport--Zink and Rapoport--Smithling--Zhang. Related to that, we also provide a moduli description for the integral models of RSZ unitary Shimura varieties in new cases. Our second result lifts the comparison of local models to categories of $p$-divisible groups and, as a corollary, to various kinds of Rapoport--Zink spaces. Our third result is a proof of the arithmetic transfer conjecture of the third author in full generality. Using our statements about Rapoport--Zink spaces, we extend the previous proof from the unramified case to that of all $p$-adic local fields ($p$ odd). |
| title | Unitary Shimura varieties at ramified primes and arithmetic transfer |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2504.17484 |