Weibel's vanishing and regularity conjecture for negative K-theory

From papers

Let XX be a Noetherian scheme of dimension dd. For a contravariant functor FF on schemes, call XX FF-regular if, for every r0r\geq 0, the map F(X)F(X×Ar)F(X)\to F(X\times\mathbb{A}^r) is an isomorphism. Weibel's conjecture.

Km(X)=0for m<d,K_m(X)=0\quad\text{for }m<-d,

and XX is KdK_{-d}-regular. This predicts vanishing of algebraic KK-theory below the negative of the dimension together with regularity in the boundary degree. It is proved for schemes essentially of finite type over a field of characteristic zero, but remains open in characteristic p>0p>0 except for curves and surfaces.

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Sources & referencesView supporting material

Primary source

G. Cortiñas, C. Haesemeyer, M. Schlichting and C. A. Weibel, “Cyclic homology, cdh-cohomology and negative K-theory”, arXiv:math/0502255 (2005).

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