CM points have everywhere good reduction

2024/10/02 by Bakker, Benjamin, Tsimerman, Jacob
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.02008

Abstract

We prove that for every Shimura variety S, there is an integral model S such that all CM points of S have good reduction with respect to S. In other words, every CM point is contained in S(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 ℓ) as being those that extend to integral points of S.

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