2023/07/01 by Nuno Hultberg, Hultberg, Nuno
Mathematics · Medicine · #11G15 #11G50 #11R04 #14G40 #Abelian group #Abelian variety #Algebraic Geometry and Number Theory #Algebraic number #Algebraic number field #Bounded function #Computer science #Degree (music) #Discrete mathematics #Extension (predicate logic) #FOS: Mathematics #Field (mathematics) #Finitely-generated abelian group #Function (biology) #Geometry #Line bundle #Magnolia and Illicium research #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Physics #Point (geometry) #Projective variety #Pure mathematics #Variety (cybernetics)
paper · pdf · doi:10.48550/arxiv.2307.00297
openalex publication_date 2023/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a projective variety over a number field K endowed with a height function associated to an ample line bundle on X. Given an algebraic extension F of K with a sufficiently big Northcott number, we can show that there are finitely many cycles in X_ℚ of bounded degree defined over F. Fields F with the required properties were explicitly constructed in arXiv:2107.09027 and arXiv:2204.04446, motivating our investigation. We point out explicit specializations to canonical heights associated to abelian varieties and selfmaps of ℙn. We apply similar methods to the study of CM-points. As a crucial tool, we introduce a refinement of Northcott's theorem.