Definition 10.135.5. Let $R \to S$ be a ring map. We say that $R \to S$ is a relative global complete intersection if there exists a presentation $S = R[x_1, \ldots , x_ n]/(f_1, \ldots , f_ c)$ and every nonempty fibre of $\mathop{\mathrm{Spec}}(S) \to \mathop{\mathrm{Spec}}(R)$ has dimension $n - c$. We will say “let $S = R[x_1, \ldots , x_ n]/(f_1, \ldots , f_ c)$ be a relative global complete intersection” to indicate this situation.

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