arXiv subjects
Publications and source records attributed to C. A. Weibel.
There is a Chern character from K-theory to negative cyclic homology. We show that it preserves the decomposition coming from Adams operations, at least in characteristic 0. This is done by using infinitesimal cohomology to reduce to the case of a nilpotent ideal (which had been established by Cathelineau some time ago).
In this paper we prove that for an affine scheme essentially of finite type over a field $F$ and of dimension $d$, $K_{d+1}$-regularity implies regularity, assuming that the characteristic of $F$ is zero. This verifies a conjecture of Vorst.
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.