Let K denote a number field, S a finite set of places of K, and ϕ: ℙⁿ → ℙⁿ a rational morphism defined over K. The main result of this paper states 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-1-6,
author = {Brian Justin Stout},
title = {A dynamical Shafarevich theorem for twists of rational morphisms},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {69-80},
zbl = {06360641},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-1-6}
}
Brian Justin Stout. A dynamical Shafarevich theorem for twists of rational morphisms. Acta Arithmetica, Tome 166 (2014) pp. 69-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-1-6/