2 problems

Let $K$ be a field and let $f\in K[x]$ be a polynomial of degree $d\geq 2$. Assume either that $\operatorname{char}(K)=0$ or that $\operatorname{char}(K)$ does not divide the local…

Let $f\in \mathbb{C}[x]$ be a complex polynomial, and let $G_\infty(\mathbb{C},f,t)$ denote its geometric iterated Galois group over a transcendental parameter $t$. A polynomial is…