Weibel's conjecture

In mathematics, Weibel's conjecture gives a criterion for vanishing of negative algebraic K-theory groups. The conjecture was proposed by and proven in full generality by  using methods from derived algebraic geometry. Previously partial cases had been proven by , ,, , and .

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 < &minus;d:


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

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


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