Roots of unity and higher ramification in iterated extensions

Spencer Hamblen, Rafe Jones

Given a field $K$, a rational function $\varphi \in K(x)$, and a point $b\in {\mathbb{P}}^1(K)$, we study the extension $K({\varphi }^{-\infty }(b))$ generated by the union over $n$ of all solutions…