Abstract
Let K be an algebraic number field and B≥1. For an endomorphism φ:Pn→Pn defined over K of degree d let Rφ⊂OK denote its minimal resultant ideal. For a fixed height function hMdn on the moduli space of dynamical systems this paper shows that all such morphisms φ of bounded resultant NK/Q(Rφ)≤B and bounded height hMdn(〈φ〉)≤B are contained in finitely many PGLn+1(K)-equivalence classes. This answers a question of Silverman in the affirmative.
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