Toric schemes and integral models for Shimura varieties with $Γ_1(p)$-type level
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911573228912640 |
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| author | Pappas, Georgios Rapoport, Michael |
| author_facet | Pappas, Georgios Rapoport, Michael |
| contents | We propose a conjectural theory of $p$-integral models of Shimura varieties with level structure at $p$ given by a class of normal subgroups of parahoric subgroups with abelian quotient group. The role of the theory of local models is played in this context by a certain root stack over the local model for parahoric level. The construction of this root stack is based on the "divisor theorem" (a foundational fact about local models) and on the theory of toric varieties in this context, both of which are of independent interest. We prove our conjecture in the case of Shimura varieties of PEL type when the parahoric is an Iwahori (under some additional conditions). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toric schemes and integral models for Shimura varieties with $Γ_1(p)$-type level Pappas, Georgios Rapoport, Michael Algebraic Geometry Number Theory Representation Theory 11G18, 14G35, 14M25 We propose a conjectural theory of $p$-integral models of Shimura varieties with level structure at $p$ given by a class of normal subgroups of parahoric subgroups with abelian quotient group. The role of the theory of local models is played in this context by a certain root stack over the local model for parahoric level. The construction of this root stack is based on the "divisor theorem" (a foundational fact about local models) and on the theory of toric varieties in this context, both of which are of independent interest. We prove our conjecture in the case of Shimura varieties of PEL type when the parahoric is an Iwahori (under some additional conditions). |
| title | Toric schemes and integral models for Shimura varieties with $Γ_1(p)$-type level |
| topic | Algebraic Geometry Number Theory Representation Theory 11G18, 14G35, 14M25 |
| url | https://arxiv.org/abs/2602.23245 |