The Stacks project

Example 29.6.4. If $A \to B$ is a ring map with kernel $I$, then the scheme theoretic image of $\mathop{\mathrm{Spec}}(B) \to \mathop{\mathrm{Spec}}(A)$ is the closed subscheme $\mathop{\mathrm{Spec}}(A/I)$ of $\mathop{\mathrm{Spec}}(A)$. This follows from Lemma 29.6.3.

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View Example 29.6.4 as pdf