Lemma 10.26.3. Let $R$ be a ring. Let $\mathfrak p \subset R$ be a prime.

the set of irreducible closed subsets of $\mathop{\mathrm{Spec}}(R)$ passing through $\mathfrak p$ is in one-to-one correspondence with primes $\mathfrak q \subset R_{\mathfrak p}$.

The set of irreducible components of $\mathop{\mathrm{Spec}}(R)$ passing through $\mathfrak p$ is in one-to-one correspondence with minimal primes $\mathfrak q \subset R_{\mathfrak p}$.

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