locally is enough

Thanks to Hao Peng
https://stacks.math.columbia.edu/tag/0BW4#comment-7483
https://stacks.math.columbia.edu/tag/0BW4#comment-7484

discriminant.tex

@@ -1523,7 +1523,8 @@ \section{The different}
 
 \begin{definition}
 \label{definition-different}
-Let $f : Y \to X$ be a flat quasi-finite morphism of Noetherian schemes.
+Let $f : Y \to X$ be a flat locally quasi-finite morphism of
+locally Noetherian schemes.
 Let $\omega_{Y/X}$ be the relative dualizing module and let
 $\tau_{Y/X} \in \Gamma(Y, \omega_{Y/X})$ be the trace element
 (Remarks \ref{remark-relative-dualizing-for-quasi-finite} and