2024/07/03 by Boaz Moerman, Moerman, Boaz · 1 citation
Mathematics · #11G35 (Secondary) #14G05 #14G12 (Primary) #14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2407.03048
openalex publication_date 2024/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a general framework for studying special subsets of rational points on an algebraic variety, termed M-points. The notion of M-points generalizes the concepts of integral points, Campana points and Darmon points. We introduce and study M-approximation over number fields and function fields, which is a notion that generalizes weak and strong approximation. We show that this property implies that the set of M-points is not thin. We then give a simple characterisation of when a split toric variety satisfies M-approximation, generalizing work of Nakahara and Streeter. Further, we determine when the set of M-points on a split toric variety is thin.