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Cyclic homology, cdh-cohomology and negative K-theory

G. Cortiñas·C. Haesemeyer·M. Schlichting·C. A. Weibel
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Abstract

We prove a blow-up formula for cyclic homology which we use to show that infinitesimal $K$-theory satisfies $cdh$-descent. Combining that result with some computations of the $cdh$-cohomology of the sheaf of regular functions, we verify a conjecture of Weibel predicting the vanishing of algebraic $K$-theory of a scheme in degrees less than minus the dimension of the scheme, for schemes essentially of finite type over a field of characteristic zero.

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G. Cortiñas, C. Haesemeyer, M. Schlichting, C. A. Weibel. 2005-02-12. Cyclic homology, cdh-cohomology and negative K-theory. https://arxiv.org/abs/math/0502255

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