A dynamical Shafarevich theorem for twists of rational morphisms

2013/08/22 by Stout, Brian
#37P15 (Secondary) #37P45 (Primary) 14G25 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1308.4992

Abstract

Let K denote a number field and a finite set S of places of K and ϕ:\PPⁿ→\PPⁿ be rational morphism defined over K. The main result of this paper proves that there are only finitely many twists of ϕ defined over K which have good reduction at all places outside S. This answers a question of Silverman in the affirmative.

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