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## A dynamical Shafarevich theorem for twists of rational morphisms

### Tom 166 / 2014

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

#### Streszczenie

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.

#### Autorzy

• Brian Justin StoutDepartment of Mathemaics