The Stacks project

Lemma 92.8.4. The cotangent complex $L_{B/A}$ is zero in each of the following cases:

1. $A \to B$ and $B \otimes _ A B \to B$ are flat, i.e., $A \to B$ is weakly étale (More on Algebra, Definition 15.104.1),

2. $A \to B$ is a flat epimorphism of rings,

3. $B = S^{-1}A$ for some multiplicative subset $S \subset A$,

4. $A \to B$ is unramified and flat,

5. $A \to B$ is étale,

6. $A \to B$ is a filtered colimit of ring maps for which the cotangent complex vanishes,

7. $B$ is a henselization of a local ring of $A$,

8. $B$ is a strict henselization of a local ring of $A$, and

9. add more here.