I come across this question which I have trouble understanding. It says
(7.3F) Suppose $Z$ is a closed subset of an affine scheme $Spec A$ locally cut out by one equation, (In other words, $Spec A$ can be covered by smaller open sets and on each such set $Z$ is cut out by one equation...
Question: Does he mean to say that there exists a smaller affine open set $U=Spec\ C$ (for example) such that $U\cap Z$ is something of the form $Spec\ (C/(g))$ for some $g\in C$. Otherwise what can this possibly mean if we do not assume that $U$ is affine?