Unramified cohomology and rationality problems (following E. Peyre)

In this talk we will discuss the question of stable rationality of the quotient $W/G$, where $W$ is a faithful complex representation of a finite group $G$. The main goal is to construct an example of representation for which the 3-rd unramified cohomology group of the field $\mathbb{C}(W)^G$ is not trivial (hence, the quotient is not stably rational), but the 2-nd group (unramified Brauer group) is trivial.