CM points have everywhere good reduction

Benjamin Bakker; Jacob Tsimerman

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arXiv · 2410.02008

CM points have everywhere good reduction

Benjamin Bakker·Jacob Tsimerman

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Abstract

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 $\mathcal{S}$.

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BibTeX RIS

Benjamin Bakker, Jacob Tsimerman. 2024-10-02. CM points have everywhere good reduction. https://arxiv.org/abs/2410.02008

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