Filtrations, mixed complexes, and cyclic homology in mixed characteristic

Abstract

In [5], we computed the cyclic homology of finite extensions of Dedekind domains. The crucial result was a formula for the cyclic homology, relative to a ground ring R, of A = R[x]/(P (x)). This paper presents two extensions of the methods and results of this paper. Recall that Hochschild homology, though generally defined in terms of a bar complex, is almost never, in practice, computed from it. A smaller complex, often a direct summand (Y·, bY ) of the reduced Hochschild complex (X·, b), is usually used. For example, it is well known (cf., e.g., [2], [11], [12]) that the Hochschild homology of A = R[x]/(P (x)) is the homology of the periodic complex