= Galois-preserving Hilbert specialization
{c}
For a <Finite Galois extension> $E/K(T)$, take a primitive element and exclude all ramification and denominator problems. A <Hilbert subset> keeping its minimal <polynomial> irreducible has residue degree $[E:K(T)]$. The residue group is an unramified decomposition subgroup of the generic <Galois group> with the same order, so it is the whole group. This specializes a regular Galois realization over $K(T)$ to realizations over $K$ when $K$ is <Hilbertian>.
Back to article page
