The Stacks project

Example 31.18.8. Here is an example of a relative effective Cartier divisor $D$ where the ambient scheme is not flat in a neighbourhood of $D$. Namely, let $A = k[t]$ and

Then $B$ is not flat over $A$ but $B/xB \cong A$ is flat over $A$. Moreover $x$ is a nonzerodivisor and hence defines a relative effective Cartier divisor in $\mathop{\mathrm{Spec}}(B)$ over $\mathop{\mathrm{Spec}}(A)$.