The Stacks project

Definition 26.5.2. Let $R$ be a ring.

  1. A standard open covering of $\mathop{\mathrm{Spec}}(R)$ is a covering $\mathop{\mathrm{Spec}}(R) = \bigcup _{i = 1}^ n D(f_ i)$, where $f_1, \ldots , f_ n \in R$.

  2. Suppose that $D(f) \subset \mathop{\mathrm{Spec}}(R)$ is a standard open. A standard open covering of $D(f)$ is a covering $D(f) = \bigcup _{i = 1}^ n D(g_ i)$, where $g_1, \ldots , g_ n \in R$.

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View Definition 26.5.2 as pdf