Journal article

Cyclic homology, cdh-cohomology and negative K-theory

G Cortinas, C Haesemeyer, M Schlichting, C Weibel

ANNALS OF MATHEMATICS | ANNAL MATHEMATICS | Published : 2008

Abstract

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.

Grants

Awarded by ANPCyT


Awarded by MEC


Awarded by RTN Network


Awarded by NSA


Funding Acknowledgements

Cortinas research was partially supported by the Ramon y Cajal fellowship, by ANPCyT grant PICT 03-12330 and by MEC grant MTM00958. Haesemeyer's research was partially supported by the Bell Companies Fellowship and RTN Network HPRN-CT-2002-00287. Schlichting's research was partially supported by RTN Network HPRN-CT-2002-00287. Weibel's research was partially supported by NSA grant MSPF-04G-184.