Abstract
We show that if X is a d-dimensional scheme of finite type over an infinite perfect field k of characteristic p > 0 , then K i ( X ) = 0 and X is K i -regular for i < − d − 2 whenever the resolution of singularities holds over k. This proves the K-dimension conjecture of Weibel [C. Weibel, K-theory and analytic isomorphisms, Invent. Math. 61 (1980) 177–197, 2.9] (except for − d − 1 ⩽ i ⩽ − d − 2 ) in all characteristics, assuming the resolution of singularities.
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