Uniform boundedness for rational points

1996/01/05 by Patricia L. Pacelli, Pacelli, Patricia L.
Mathematics · #14G05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.alg-geom/9601004

openalex publication_date 1996/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend an earlier result by Dan Abramovich, showing that a conjecture of S. Lang's implies the existence of a uniform bound on the number of K-rational points over all smooth curves of genus g defined over K, where K is any number field of fixed degree d, and g is an integer greater than 1. The bound depends only on the genus g and the degree of the number field K.

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