Cyclic homology, cdh-cohomology and negative K-theory

• Autores: Guillermo Cortiñas , Christian Haesemeyer, Marco Schlichting , Charles A. Weibel
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 167, Nº 2, 2008, págs. 549-573
• Idioma: inglés
• DOI: 10.4007/annals.2008.167.549
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• Resumen

  • 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.