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Let G be an affine group scheme, and Dist(G) its hyperalgebra.

I am wondering what is the relationship between Dist(G) and G interms of Cohomology?

Is there a cohomology theory for Dist(G), if so what information does it give?

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Do you have Jantzens book "Representations of Algebraic Groups"? Chapter I.7 is all about $\mathrm{Dist}(G)$. –  Jim Sep 24 '13 at 23:07
    
I do (infact I just started reading I.7 tonight) though I was especially wondering \textit{(a priori)} since $Dist(G)=Lie(G)$ in the case of a field of characteristic 0. Then, is there an explicit relationship between the lia lagebra cohomology of Lie(G) and the rational cohomology of G. –  CSA Sep 25 '13 at 3:36

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