2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150050A singular curve over a non-perfect field K may not have a smooth model over K. Those are said to "change genus". If K is a global field of positive characteristic and C/K a curve that change genus, then C(K) is known to be finite. The purpose of this note is to give examples of curves with fixed relative genus, defined over K for which #C(K) is arbitrarily large. The motivation for considering this problem comes from the work of Caporaso et al. [CHM], where they show that a conjecture of Lang implies that, for a number field K, #C(K) can be bounded in terms of g and K only for all curves C/K of genus g > 1.plain TeXAlgebraic Geometry14G25 (Primary) 11G30 (Secondary)text