Let \(K\) be a field of characteristic zero, \(R = K[X_1, \ldots, X_N]\), and \(F\) a reduced polynomial in \(R\). Then \(A = R/(F(X_1, \ldots, X_N))\) is a reduced affine hypersurface. The author proves that the Hodge-components of the Hochschild homology of \(A\) are given by torsion modules of Kähler differentials. The author also obtains a new vanishing result for the Hodge-components of the cyclic homology of affine hypersurfaces and gives an explicit computation of these Hodge- components of the cyclic homology in the case of a hypersurface defined by a quasi-homogeneous polynomial.
For the entire collection see [Zbl 0809.00016].