Lemma 27.18.3. Let $X$ be a scheme. Let $f \in \Gamma (X, \mathcal{O}_ X)$. Assume $X$ is quasi-compact and quasi-separated and assume that $X_ f$ is affine. Then the canonical morphism

from Schemes, Lemma 25.6.4 induces an isomorphism of $X_ f = j^{-1}(D(f))$ onto the standard affine open $D(f) \subset \mathop{\mathrm{Spec}}(\Gamma (X, \mathcal{O}_ X))$.

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