# Hochschild (co)homology and Kahler differentials

Suppose $A$ is an augmented commutative algebra over a field $k$. What is the relation between Hochschild homology $H_n(A,k)$ and Kahler differential $\Omega_{A/k}$? The same question is also asked about $H^n(A,k)$ and $\Omega_{A/k}$. Here $k$ is considered as the trivial $A$-bimodule via the augmentation.

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can HKR be globalised to schemes? –  Jacob Bell Mar 20 '13 at 15:14
Thanks for referring to the HKR. –  Xingting Mar 25 '13 at 17:24