  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.
