Cyclic homology, cdh-cohomology and negative K-theory

Details Cyclic homology, cdh-cohomology and negative K-theory Cyclic homology, cdh-cohomology and negative K-theory

2005-02-12

arxiv.org/abs/math/0502255v1

Ann. Math. 167, (2008) 549-573

Mathematics

K-Theory and Homology

20 pages, amslatex, uses xypic

Scientific paper

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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