Quelques considérations galoisiennes relatives à l’extension des constantes d’un corps de fractions tordu

In this article, we state several results relating to the arithmetic of a constants extension of a skew fractions field $K[t,\sigma ,\delta ]$. As an application, we show a non-commutative version of the Leptin–Waterhouse theorem: for any profinite group $\Gamma$, there exist a skew field $K$ and an algebraic, outer and Galois extension $L/K$ such that $\text{Gal}(L/K)\simeq \Gamma$.