Uniformity of rational points: an up-date and corrections

The purpose of this note is to correct, and enlarge on, an argument in a paper we published a quarter century ago (J. Amer. Math. Soc. 10:1 (1997), 1–35). The question raised is a simple one to state: given that a curve $C$ of genus $g \geq 2$ defined over a number field $K$ has only finitely many rational points, we ask if the number of points is bounded as $C$ varies.

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Keywords

rational points, uniformity

Mathematical Subject Classification

Primary: 14G05, 14H10

Milestones

Received: 14 June 2021

Revised: 13 July 2021

Accepted: 28 July 2021

Published: 30 March 2022

Authors

Lucia Caporaso
Department of Mathematics and Physics Roma TRE University Rome Italy

Joe Harris
Department of Mathematics Harvard University Cambridge, MA United States

Barry Mazur
Department of Mathematics Harvard University Cambridge, MA United States

Vol. 4, No. 1, 2022

Lucia Caporaso, Joe Harris and Barry Mazur

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors