Cyclic homology, cdh-cohomology and negative K-theory

TY - JOUR

T1 - Cyclic homology, cdh-cohomology and negative K-theory

AU - Cortiñas, G.

AU - Haesemeyer, C.

AU - Schlichting, M.

AU - Weibel, C.

PY - 2008/3

Y1 - 2008/3

N2 - 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.

AB - 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.

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U2 - 10.4007/annals.2008.167.549

DO - 10.4007/annals.2008.167.549

M3 - Article

SN - 0003-486X

VL - 167

SP - 549

EP - 573

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

ER -