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
\[ B = k[t, x, y, x^{-1}y, x^{-2}y, \ldots ]/(ty, tx^{-1}y, tx^{-2}y, \ldots ) \]
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 $\mathop{\mathrm{Spec}}(A)$.
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