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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"

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    [This question on MathOverflow](http://mathoverflow.net/questions/36486/standard-reduction-to-the-artinian-local-case) seems to be closely related to what you're looking for (unfortunately I don't understand it myself). If it's what you're looking for, I can make this an answer.2012-03-28
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    that was the kind of answer I was looking for2012-03-29

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