2024/09/09 by Maarten Derickx, Derickx, Maarten
Computer Science · Engineering · Mathematics · #11G30 #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Digital Image Processing Techniques #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2409.05796
openalex publication_date 2024/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A number field K is called primitive if \mathbb Q and K are the only subfields of K. Let X be a nice curve over \mathbb Q of genus g. A point P of degree d on X is called primitive if the field of definition \mathbb Q(P) of the point is primitive. In this short note we prove that if X has a divisor of degree d> 2g, then X has infinitely many primitive points of degree d. This complements the results of Khawaja and Siksek that show that points of low degree are not primitive under certain conditions.