# Cyclic homology, cdh-cohomology and negative $K$-theory

### Abstract

We prove a blow-up formula for cyclic homology which we use to show that infinitesimal $K$-theory satisfies ${\rm cdh}$-descent. Combining that result with some computations of the ${\rm cdh}$-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.

## Authors

Guillermo Cortiñas

Dept. de Álg. y Geom. y Top.
Spain

Christian Haesemeyer

Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Chicago, IL 60607
United States

Marco Schlichting

Department of Mathematics
Louisiana State University
Baton Rouge, LA 70803
United States

Charles Weibel

Department of Mathematics
Rutgers University
New Brunswick, NJ 08854
United States