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

Guillermo Cortiñas; Christian Haesemeyer; Marco Schlichting; Charles Weibel

doi:10.4007/annals.2008.167.549

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

Pages 549-573 from Volume 167 (2008), Issue 2 by Guillermo Cortiñas, Christian Haesemeyer, Marco Schlichting, Charles Weibel

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.

Mathematical Subject Classification

Primary 2000: 19D35, 19D55

DOI

https://doi.org/10.4007/annals.2008.167.549

2415380

zbMATH

1191.19003

Milestones

Received: 3 March 2005
Accepted: 16 January 2007
Published online: 1 March 2009