Local cyclic homology (Q2639167)

This paper deals with cyclic homology in the spirit of the algebraic de Rham cohomology of a formal neighborhood. Local (cyclic) homology of filtered associative algebras is defined and discussed. In the commutative case, it is shown that the canonical homomorphism of filtered algebraic \(S^ 1\)-chain complexes C*(A)\(\to \lim_{\leftarrow k}C*(A/I_ k)\) induces an isomorphism \(\hat C*(A)=\lim_{\leftarrow p}C*(A)/F_ pC*(A)\to \lim_{\leftarrow k}C*(A/I_ k)\). This result enables the author to obtain a sort of generalization of a result of Feigin and Tsygan on periodic homology. It is also shown that for a filtered k-algebra A with filtration HC-cofinite, the F-filtration on \({}_ B\hat C*(A)\) is strongly convergent.