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