Definition 10.149.2. Let $R \to S$ be a formally unramified ring map.

1. The universal first order thickening of $S$ over $R$ is the surjection of $R$-algebras $S' \to S$ of Lemma 10.149.1.

2. The conormal module of $R \to S$ is the kernel $I$ of the universal first order thickening $S' \to S$, seen as an $S$-module.

We often denote the conormal module $C_{S/R}$ in this situation.

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