Geodesic
Cyclic homology, cdh-cohomology and negative $K$-theory
Guillermo Cortiñas1 ; Christian Haesemeyer2 ; Marco Schlichting3 ; Charles Weibel4
1 Dept. de Álg. y Geom. y Top.<br/>Universidad de Valladolid<br/>47005 Valladolid<br/>Spain
2 Department of Mathematics, Statistics, and Computer Science<br/>University of Illinois at Chicago<br/>Chicago, IL 60607<br/>United States
3 Department of Mathematics<br/>Louisiana State University<br/>Baton Rouge, LA 70803<br/>United States
4 Department of Mathematics<br/>Rutgers University<br/>New Brunswick, NJ 08854<br/>United States
Annals of mathematics, Tome 167 (2008) no. 2, pp. 549-573

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.

DOI : 10.4007/annals.2008.167.549

Guillermo Cortiñas 1 ; Christian Haesemeyer 2 ; Marco Schlichting 3 ; Charles Weibel 4

1 Dept. de Álg. y Geom. y Top.<br/>Universidad de Valladolid<br/>47005 Valladolid<br/>Spain
2 Department of Mathematics, Statistics, and Computer Science<br/>University of Illinois at Chicago<br/>Chicago, IL 60607<br/>United States
3 Department of Mathematics<br/>Louisiana State University<br/>Baton Rouge, LA 70803<br/>United States
4 Department of Mathematics<br/>Rutgers University<br/>New Brunswick, NJ 08854<br/>United States 
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Guillermo Cortiñas; Christian Haesemeyer; Marco Schlichting; Charles Weibel. Cyclic homology, cdh-cohomology and negative $K$-theory. Annals of mathematics, Tome 167 (2008) no. 2, pp. 549-573. doi: 10.4007/annals.2008.167.549

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