A Uniform Field-of-Definition/Field-of-Moduli Bound for Dynamical Systems on ${\mathbf{P}}^N$

Abstract

Let $f:{\mathbb{P}}^N\to {\mathbb{P}}^N$ be an endomorphism of degree $d\ge 2$ defined over $\overline{\mathbb{Q}}$ or ${\overline{\mathbb{Q}}}_p$, 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 $d$.

arXiv comment22 pages

References in corpus (1)

• Questions on self maps of algebraic varieties