Hodge-components of cyclic homology for affine quasi-homogeneous hypersurfaces. (English) Zbl 0832.14005
Kassel, Christian (ed.) et al., \(K\)-theory. Contributions of the international colloquium, Strasbourg, France, June 29-July 3, 1992. Paris: Société Mathématique de France, Astérisque. 226, 321-333 (1994).
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].
For the entire collection see [Zbl 0809.00016].
Reviewer: Li Fuan (Beijing)
MSC:
14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
19D55 | \(K\)-theory and homology; cyclic homology and cohomology |
14J70 | Hypersurfaces and algebraic geometry |