A dynamical Shafarevich theorem for twists of rational morphisms

Brian Stout

A dynamical Shafarevich theorem for twists of rational morphisms

Number Theory 2013-08-30 v2 Dynamical Systems

Authors: Brian Stout

Abstract

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

Keywords

Shafarevich theorem dynamical systems rational morphisms twists good reduction number fields Silverman's question

Cite

@article{arxiv.1308.4992,
  title  = {A dynamical Shafarevich theorem for twists of rational morphisms},
  author = {Brian Stout},
  journal= {arXiv preprint arXiv:1308.4992},
  year   = {2013}
}

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