Profinite Iterated Monodromy Groups of Unicritical Polynomials

Ophelia Adams; Trevor Hyde

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arXiv · 2504.13028

Profinite Iterated Monodromy Groups of Unicritical Polynomials

Ophelia Adams·Trevor Hyde

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Abstract

Let $f(x) = ax^d + b \in K[x]$ be a unicritical polynomial with degree $d \geq 2$ which is coprime to $\mathrm{char} K$. We provide an explicit presentation for the profinite iterated monodromy group of $f$, analyze the structure of this group, and use this analysis to determine the constant field extension in $K(f^{-\infty}(t))/K(t)$.

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Ophelia Adams, Trevor Hyde. 2025-04-17. Profinite Iterated Monodromy Groups of Unicritical Polynomials. https://arxiv.org/abs/2504.13028

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