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
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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

Generalization

Recently, have generalized Weibel's conjecture to arbitrary quasi-compact quasi-separated derived schemes. In this formulation the Krull dimension is replaced by the valuative dimension. In the case of Noetherian schemes, the Krull dimension is equal to the valuative dimension.