For a given endomorphism on a unitary k-algebra, A, with k in the center of A, there are definitions of twisted cyclic and Hochschild homology. This paper will show that the method used to define them can be used to define twisted de Rham homology. The main result is that twisted de Rham homology can be thought of as the kernel of the Connes map from twisted cyclic homology to twisted Hochschil...

We prove that the cyclic homology of a scheme with an ample line bundle coincides with the cyclic homology of its category of algebraic vector bundles. As a byproduct of the proof, we obtain a new construction of the Chern character of a perfect complex on a ringed space. 1991 Mathematics Subject Classi cation: Primary: 16E40; Secondary: 18E30, 14F05.

We prove that the cyclic homology of a scheme with an ample line bundle coincides with the cyclic homology of its category of algebraic vector bundles. As a byproduct of the proof, we obtain a new construction of the Chern character of a perfect complex on a ringed space. Subject classification: 16E40 (Primary), 18E30, 14F05 (Secondary).

In this paper we prove that cyclic homology, topological cyclic homology, and algebraic K-theory satisfy a pro Mayer–Vietoris property with respect to abstract blow-up squares of varieties, in both zero and finite characteristic. This may be interpreted as the well-definedness of K-theory with compact support.

Cuntz and Quillen have shown that for algebras over a field k with char(k) = 0, periodic cyclic homology may be regarded, in some sense, as the derived functor of (non-commutative) de Rham (co-)homology. The purpose of this paper is to formalize this derived functor analogy. We show that the localization DefPA of the category PA of countable pro-algebras at the class of (infinitesimal) deformat...

Given a compact manifold $M$ and $g\in C^{\infty}(M,U(l;\mathbb{C}))$ we construct Chern character $\mathrm{Ch}^-(g)$ which lives in the odd part of equivariant (entire) cyclic Chen-normalized bar complex $\underline{\mathscr{C}}(\Omega_{\mathbb{T}}(M\times \mathbb{T}))$ $M$, is mapped to Bismut-Chern under Chen integral map. It also shown that assignment $g\mapsto \mathrm{Ch}^-(g)$ induces wel...

In this paper we show that to a unital associative algebra object (resp. co-unital coassociative co-algebra object) of any abelian monoidal category (C,⊗) endowed with a symmetric 2-trace, i.e. an F ∈ Fun(C,Vec) satisfying some natural trace-like conditions, one can attach a cyclic (resp. cocyclic) module, and therefore speak of the (co)cyclic homology of the (co)algebra “with coefficients in F...