Title: Galois extensions of function fields and the Tchebotarev property Speaker: Pierre Debes (Lille 1) Abstract: This is a joint work with Sara Checcoli. We extend the Tchebotarev property of number field extensions to function field extensions over certain base fields. Our base fields include number fields, p-adic fields, finite fields, PAC fields., etc. I will show that this property is the core of some local-global properties of infinite Galois extensions and explain its connection with the Hilbert specialization property and the Grunwald problem.