Uniformity of rational points over all quadratic fields

1994/11/24 by Dan Abramovich, Abramovich, Dan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9411015

4 pages, LaTeX. "Final" version. Urges of doubters of people's sense of humor followed; jokes removed. Jokes available from author upon request

openalex publication_date 1994/11/24 · arxiv created 1994/12/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We refine a result of L. Caporaso, J. Harris and B. Mazur, and prove: Supposons que la conjecture de Lang soit vraie. Soit K un corps des nombres et g>1 un entier. Il existe un nombre N(K,g) tel que si L est une extension de degré ≤ 3 de K et C est une courbe lisse projective connèxe, de genre g définie sur L on a # C(L) < N(K,g).

Related

• Lang's conjectures, Conjecture H, and uniformity
• Uniform boundedness for rational points
• On the number of rational points on special families of curves over function fields
• Bounds on the number of rational points of curves in families
• Remarks about uniform boundedness of rational points over function fields