Hi,

Let $R$ be a $\mathbb Q$-algebra and let $A$ be a smooth $R$-algebra. If $A$ is a polynomial algebra $A = R[T_1,\dots,T_n]$, then it is easy to see that the natural map $R \to \Omega^\bullet_{A/R}$ is a quasi-isomorphism of $R$-modules.

Question: is the same true for $A$ a smooth $R$-algebra if there is an etale map $F\to A$ with $F = R[T_1,\dots,T_n]$ (this is always the case locally on $A$)?

Thanks!