A dynamical Shafarevich theorem for twists of rational morphisms (Q2925470)

Let \(k\) be a number field, \(S\) a finite set of places of \(k\). Shafarevich famously conjectured -- and proved! -- that there were only finitely many isomorphism classes of elliptic curves over \(k\) that had good reduction outside of \(S\). Since then, many authors have extended this result to other classes of arithmetic varieties, and the paper under review falls into this category, albeit with a dynamical twist.NEWLINENEWLINENEWLINENEWLINEIn this paper, the author answers a question of Silverman, by proving that there are only finitely many twists of a given rational morphism from \(\mathbb{P}^n\) to itself with good reduction outside \(S\).