Filtrations, mixed complexes, and cyclic homology in mixed characteristic (Q1895848)

The author determines mixed complexes \((Y, b_Y, B_Y)\) which compute the cyclic homology of plane curves and maximal orders in simple algebras. In each case, \((Y, b_Y)\) is a direct summand of the reduced Hochschild complex and a strongly homotopy linear map may be constructed from \((Y, b_Y, B_Y)\) to the usual mixed complex computing cyclic homology. Those results extend previous ones by the author [Homology of maximal orders in central simple algebras, Comment. Math. Helv. 67, No. 4, 613-634 (1992; Zbl 0777.16005)] and by the author and \textit{A. Lindenstrauss} [Cyclic homology of Dedekind domains, \(K\)-Theory 6, No. 4, 301-334 (1992; Zbl 0781.13008)].