REGULAR LIFTING OF COVERS OVER AMPLE FIELDS

Abstract

Let $K$ be an ample field, $G$ a finite group, and $L$ a finite Galois extension of $K$ such that $\mathrm{Gal}(L/K)$ is isomorphic to a subgroup of $G$. We prove that $K\left(x\right)$ has a Galois extension $F$ which is regular over $L$ such that $\mathrm{Gal}(F/K(x\left)\right)≌G$ and $F$ has a $K$-place $\phi$ such that $\phi \left(x\right)\in K$ and $\phi \left(F\right)=L\cup \{\infty \}$.