Lemma 51.4.8. Let $I \subset A$ be a finitely generated ideal of a ring $A$. If $\text{cd}(A, I) = 1$ then $\mathop{\mathrm{Spec}}(A) \setminus V(I)$ is nonempty affine.

Proof. This follows from Lemma 51.4.1 and Cohomology of Schemes, Lemma 30.3.1. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).