a reduction to Artinian case let $f:X\rightarrow Y$ be a proper, smooth morphism of schemes over a field $k$. In a paper I read that by "classical reduction arguments" to compute $R^pf_{*}\Omega_{X/Y}$ I can assume that $Y=Spec(A)$, where $A$ is an artinian $k$-algebra. 
I always find assertion like this. Since I realized that one cannot ask for a survey of all "reduction arguments" like this one, I decided to ask this particular case. Of course it would be nice if one had such a survey, without quoting "somewhere in EGA"

This post on MathOverflow seems to provide the survey you're looking for.
