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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.… 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 is very useful. john – john Mar 18 '13 at 17:15

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