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iam learning formal schemes. Suppose $Y\subset X$ are schemes, and $\hat{X}$ is the completion of $X$ along closed subscheme $Y$. I wondered if there is a notion of sheaf of differential forms on a formal scheme $\hat{X}$ and a 'de Rham' complex $\Omega^.$ whose cohomology has a relation with cohomology of $X$ or $Y$.

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A good place to look might be Hartshorne's paper on de Rham cohomology of algebraic varieties. archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1975__45_/… In particular, Section 1.7 defines the object you talk about, and much of the paper is devoted to the study of its cohomology. –  ChrisLazda Mar 18 '13 at 16:28
    
At least for varieties over a field of char 0 that is. –  ChrisLazda Mar 18 '13 at 16:29
    
thanks..it is very useful. john –  john Mar 18 '13 at 17:15

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