The Stacks project

When you say a "Noetherian domain of characteristic 0" do you mean the domain contains the rationals or that its fraction field has characteristic 0? I think this result holds as long as the fraction field of the domain has characteristic 0, so may be it is good to specify this in the statement?

THanks and fixed here.

From the proof we see that the condition "fraction field has characteristic zero " can be relaxed to "fraction field is perfect".

@ #7448: True, but if $R$ is a noetherian domain with perfect fraction field $K$ of char. $p>0$, then $R=K$. Otherwise, by Krull-Akizuki, there is a discrete valuation ring $V$ between $R$ and $K$, and a uniformizer of $V$ cannot be a $p$-th power in $K$. (There may be simpler arguments).