Lemma 27.29.8. Let $X$ be a scheme and $x \in X$ a point. There exists an affine open neighbourhood $U \subset X$ of $x$ such that the canonical map $\mathcal{O}_ X(U) \to \mathcal{O}_{X, x}$ is injective in each of the following cases:

$X$ is integral,

$X$ is locally Noetherian,

$X$ is reduced and has a finite number of irreducible components.

## Comments (0)