Weibel's conjecture

In mathematics, Weibel's conjecture gives a criterion for vanishing of negative algebraic K-theory groups. The conjecture was proposed by Template:Harvs. After several authors proved partial cases, it was proven in full generality by Template:Harvtxt using methods from derived algebraic geometry.

Statement of the conjecture

Weibel's conjecture asserts that for a Noetherian scheme X of finite Krull dimension d, the K-groups vanish in degrees < −d:

$K_i(X)=0\text{ for }i<-d$

and asserts moreover a homotopy invariance property for negative K-groups

$K_i(X)=K_i(X\times {𝔸}^r)\text{ for }i\le -d\text{ and arbitrary }r.$

References

• Template:Citation

• Template:Citation