Hilbertian fields and Hilbert's irreducibility theorem

Rodney Coleman (1) , Laurent Zwald (2)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 SVH - Statistique pour le Vivant et l’Homme

Hilbert's irreducibility theorem plays an important role in inverse Galois theory. In this article we introduce Hilbertian fields and present a clear detailed proof of Hilbert's irreducibility theorem in the context of these fields.

Domaines: Théorie des groupes [math.GR]

Rodney Coleman, Laurent Zwald. Hilbertian fields and Hilbert's irreducibility theorem. 2018. ⟨hal-01883575⟩