CM points have everywhere good reduction
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917793575731200 |
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| author | Bakker, Benjamin Tsimerman, Jacob |
| author_facet | Bakker, Benjamin Tsimerman, Jacob |
| contents | We prove that for every Shimura variety $S$, there is an integral model $\mathcal{S}$ such that all CM points of $S$ have good reduction with respect to $\mathcal{S}$. In other words, every CM point is contained in $\mathcal{S}(\overline{\mathbb{Z}})$. This follows from a stronger local result wherein we characterize the points of $S$ with potentially-good reduction (with respect to some auxiliary prime $\ell$) as being those that extend to integral points of $\mathcal{S}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CM points have everywhere good reduction Bakker, Benjamin Tsimerman, Jacob Number Theory Algebraic Geometry We prove that for every Shimura variety $S$, there is an integral model $\mathcal{S}$ such that all CM points of $S$ have good reduction with respect to $\mathcal{S}$. In other words, every CM point is contained in $\mathcal{S}(\overline{\mathbb{Z}})$. This follows from a stronger local result wherein we characterize the points of $S$ with potentially-good reduction (with respect to some auxiliary prime $\ell$) as being those that extend to integral points of $\mathcal{S}$. |
| title | CM points have everywhere good reduction |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2410.02008 |