Let $k$ be an algebraically closed field.
Let $B$ a $k$-algebra of finite type, normal and Cohen-macaulay. Let $G$ a finite group acting on $B$. We assume that the order of $G$ is prime to the charecteristic of $k$.
We consider $A=B^{G}$ and assume that A is smooth and connected. Let $\pi:Spec(B)\rightarrow Spec(A)$. We assume that there exists an element $t\in A$ regular such that $\pi$ is étale outside $V(t)$.
Thus by using the trace, we can define the different ideal $\delta_{B/A}\subset B$ and a discriminant ideal $\mathfrak{D}_{B/A}\subset A$ such as in Serre, Corps locaux III.
Do we always have $N_{B/A}(\delta_{B/A})=\mathfrak{D}_{B/A}$?
