1992/10/13 by Olivier Debarre, Debarre, Olivier, Matthew Klassen +1 · 2 citations
Arts and Humanities · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #French Historical and Cultural Studies #Historical Studies and Socio-cultural Analysis
paper · pdf · doi:10.48550/arxiv.alg-geom/9210004
openalex publication_date 1992/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this note is to provide some applications of Faltings' recent proof of S. Lang's conjecture to smooth plane curves. Let C be a smooth plane curve defined by an equation of degree d with integral coefficients. We show that for d≥ 7, the curve C has only finitely many points whose field of definition has degree ≤ d-2 over Q, and that for d≥ 8, all but finitely many points of C whose field of definition has degree ≤ d-1 over Q arise as points of intersection of rational lines through rational points of C.