Siegel's theorem and the abc conjecture

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97170Following N. Elkies ("ABC implies Mordell") we show that the abc conjecture of Masser-Oesterle implies an effective version of Siegel's theorem about integral points on algebraic curves, i.e. an upper bound for the S-integral points where the dependence on S is explicit. The converse statement is also announced in this note. For both results, the main geometric tool is a theorem of G.V. Belyi.10 pages; to appear in Rivista Matematica dell'Universita' di Parma, Atti del Secondo Convegno Italiano di Teoria dei NumeriNumber Theory11G30; 11J25; 11G50Siegel's theorem and the abc conjecturetext