Galois Realisations of ${\mathrm{PSL}}_2({\mathbb{F}}_{p^2})$ via non-unirational Hilbert Irreducibility

Julian Demeio, Damián Gvirtz-Chen

We establish non-unirational versions of Hilbert Irreducibility for all Hilbert modular surfaces which are of K3 type. As an application we prove new instances of the regular Inver…