Vol. 4, No. 1, 2022

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Uniformity of rational points: an up-date and corrections

Lucia Caporaso, Joe Harris and Barry Mazur

Vol. 4 (2022), No. 1, 183–201
DOI: 10.2140/tunis.2022.4.183
Abstract

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 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.

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