Profinite Iterated Monodromy Groups of Unicritical Polynomials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912333072171008 |
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| author | Adams, Ophelia Hyde, Trevor |
| author_facet | Adams, Ophelia Hyde, Trevor |
| contents | 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 $K(f^{-\infty}(t))/K(t)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Profinite Iterated Monodromy Groups of Unicritical Polynomials Adams, Ophelia Hyde, Trevor Number Theory Dynamical Systems 37P05 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 $K(f^{-\infty}(t))/K(t)$. |
| title | Profinite Iterated Monodromy Groups of Unicritical Polynomials |
| topic | Number Theory Dynamical Systems 37P05 |
| url | https://arxiv.org/abs/2504.13028 |