The Brauer group Br(k) of a field k is an important object of study in number theory. A convenient condition to force the Brauer group to be trivial is for k to be quasi-algebraically closed. Quasi-algebraically closed fields are part of a more general notion of C_i fields, introduced in Lang’s thesis in 1951. The goal of this talk is to prove that finite fields and function fields over algebraically closed fields are quasi-algebraically closed hence have trivial Brauer groups.