A Shafarevich-Faltings Theorem For Rational Functions

2006/03/17 by Szpiro, Lucien, Tucker, Thomas J.
#11G05 #14G25 #14G40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0603436

Abstract

Using an alternative notion of good reduction, an analog of the Shafarevich theorem for elliptic curves is proved for morphisms of the projective line over number fields.

Related

• A dynamical Shafarevich theorem for rational maps over number fields and function fields
• A dynamical Shafarevich theorem for twists of rational morphisms
• Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves
• Uniformly effective Shafarevich Conjecture on families of hyperbolic curves over a curve with prescribed degeneracy locus
• Complete intersections: Moduli, Torelli, and good reduction