A uniform field-of-definition/field-of-moduli bound for dynamical systems on P-N

摘要

Let f : P-N - P-N be an endomorphism of degree d = 2 defined over (Q) over bar or (Q) over bar (p), and let K be the field of moduli of f. We prove that there is a field of definition L for f whose degree [L : K] is bounded solely in terms of N and d. (C) 2018 Elsevier Inc. All rights reserved.