Weibel's dimension conjecture for negative K-theory

Let XX be a Noetherian scheme of dimension dd, and write Km(X)K_m(X) for its algebraic KK-groups. A scheme is KnK_n-regular when homotopy invariance holds in degree nn, equivalently when Kn(X)Kn(X×A1)K_n(X)\to K_n(X\times\mathbb A^1) is an isomorphism. Weibel's dimension conjecture.

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

and XX is KdK_{-d}-regular. This conjecture is a central prediction about the vanishing range and homotopy invariance of negative KK-theory; the supplied text gives no resolution status.

Sources & referencesView supporting material

Primary source

Guillermo Cortiñas, “Excision, descent, and singularity in algebraic K-theory”, arXiv:1312.1639 (2014).

Additional references

2 papers in this index state this conjecture (2008–2013). The statement above is taken from the most recent of them; the others are arXiv:0811.0302.

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