Lemma 89.8.4. The cotangent complex $L_{B/A}$ is zero in each of the following cases:

$A \to B$ and $B \otimes _ A B \to B$ are flat, i.e., $A \to B$ is weakly étale (More on Algebra, Definition 15.95.1),

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

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

$A \to B$ is unramified and flat,

$A \to B$ is étale,

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

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

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

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## Comments (2)

Comment #4517 by Manuel Hoff on

Comment #4740 by Johan on