A dynamical Shafarevich theorem for twists of rational morphisms

Brian Stout

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arXiv · 1308.4992

A dynamical Shafarevich theorem for twists of rational morphisms

Brian Stout

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Abstract

Let $K$ denote a number field and a finite set $S$ of places of $K$ and $ϕ:\PP^n\rightarrow\PP^n$ 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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Brian Stout. 2013-08-28. A dynamical Shafarevich theorem for twists of rational morphisms. https://arxiv.org/abs/1308.4992

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