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 of genus defined over a number field has only finitely many rational points, we ask if the number of points is bounded as varies.
"Uniformity of rational points an up-date and corrections." Tunisian J. Math. 4 (1) 183 - 201, 2022. https://doi.org/10.2140/tunis.2022.4.183