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Let $f:\mathbb{P}^N\to\mathbb{P}^N$ be an endomorphism of degree $d\ge2$ 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… Click to show full abstract
Let $f:\mathbb{P}^N\to\mathbb{P}^N$ be an endomorphism of degree $d\ge2$ 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 $d$.
Keywords:
field;
field moduli;
uniform field;
field definition;
definition field
Journal Title: Journal of Number Theory
Year Published: 2019
Link to full text (if available)
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Journal Title: Journal of Number Theory
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!