Cyclic homology of hypersurfaces (Q1208206)

Let \(A\) be a geometrically regular \(k\)-algebra over a characteristic zero field \(k\) and \(P\in A\) be a nonzero divisor. In [Funkts. Anal. Prilozh. 19, No. 2, 55--62 (1985; Zbl 0585.18007)], \textit{B. L. Feigin} and \textit{B. L. Tsygan} proved that the cyclic homology of \({A\over \langle P\rangle}\) is a direct sum of the homologies of the complexes \(\Omega^*(A)/F_ j\Omega^*(A)\), where \(F_ j\) is a filtration that depends on \(P\). In this paper, the authors compute explicitly the homologies of the complexes \(\Omega^*(A)/F_ j\Omega^*(A)\) in terms of de Rham homologies and differential modules of the \(k\)-algebras \(A/(p^ i)\).