On the Cyclic Homology of Ringed Spaces and Schemes

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 Classification: Primary: 16E40; Secondary: 18E30, 14F05.

Keywords: Cyclic homology, Chern character, Ringed space, Scheme, Perfect complex, Derived category.

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