Year: 2025
Type: preprint
Abstract: Let $K$ be a field complete with respect to a discrete valuation $v$ of residue characteristic $p$. For $α\in K$, let $K_\infty$ be the extension obtained by adjoining all iterated preimages of $α$ under a unicritical polynomial $f_c(z)=z^\ell - c \in K[z]$. We study the extension $K_\infty/K$ and show that its qualitative behavior depends only on the valuation of $c$. This removes the previous restrictions on $\ell$ in work of Anderson--Hamblen--Poonen--Walton and completes the classification for all $\ell \ge 2$. We also relate the ramification to the structure of the Berkovich Julia set of $f_c$.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407012851