CM points have everywhere good reduction
CM points have everywhere good reduction
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 …