Lemma 36.38.4. Let $X$ be a Noetherian regular scheme of finite dimension. Then the map $K_0(X) \to K'_0(X)$ is an isomorphism.
Proof. Follows immediately from Lemma 36.11.8 and our construction of the map $K_0(X) \to K'_0(X)$ above. $\square$
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