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A dynamical Shafarevich theorem for twists of rational morphisms

Volume 166 / 2014

Brian Justin Stout Acta Arithmetica 166 (2014), 69-80 MSC: Primary 37P45; Secondary 14G25, 37P15. DOI: 10.4064/aa166-1-6


Let $K$ denote a number field, $S$ a finite set of places of $K$, and $\phi :\mathbb {P}^n\rightarrow \mathbb {P}^n$ a rational morphism defined over $K$. The main result of this paper states that there are only finitely many twists of $\phi $ defined over $K$ which have good reduction at all places outside $S$. This answers a question of Silverman in the affirmative.


  • Brian Justin StoutDepartment of Mathemaics
    U.S. Naval Academy
    Chauvenet Hall
    Annapolis, MD, 21401-1363, U.S.A.

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