Definition 10.143.1. Let $R \to S$ be a ring map. We say $R \to S$ is *étale* if it is of finite presentation and the naive cotangent complex $\mathop{N\! L}\nolimits _{S/R}$ is quasi-isomorphic to zero. Given a prime $\mathfrak q$ of $S$ we say that $R \to S$ is *étale at $\mathfrak q$* if there exists a $g \in S$, $g \not\in \mathfrak q$ such that $R \to S_ g$ is étale.

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