Hilbert's Irreducibility for ${\mathbb{G}}_m$

Michael Stoll, Samir Siksek

Let $K$ be a number field and $S$ a finite set of non-archimedean places. Write ${\mathcal{O}}_S$ for the ring of $S$-integers of $K$ and ${\mathcal{O}}_S^{\times }$ for its unit group. L…