1995/06/06 by José Felipe Voloch, Voloch, Jose' Felipe
Arts and Humanities · Mathematics · Social Sciences · #14G25 (Primary) 11G30 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Communism, Protests, Social Movements #FOS: Mathematics #French Historical and Cultural Studies
paper · pdf · doi:10.48550/arxiv.alg-geom/9506009
openalex publication_date 1995/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 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.