We'll discuss recent results in inverse Galois theory and Field Arithmetic.
We'll show that every finite group occurs as an automorphism group over any Hilbertian field.
This generalizes previous theorems of Fried and Takahashi for number fields and global fields.
Building upon this result, we show that every finite split embedding problem over any Hilbertian field admits
a not-necessarily-Galois pseudo-solution.
This proves a necessary consequence of the Debes-Deschamps Conjecture.
Joint work with Francois Legrand and Arno Fehm.