Recall that a morphism of schemes $X\rightarrow Y$ is regular if it's flat with geometric fibres that are regular schemes.

Fix a field $k$ and consider a morphism $f:X\rightarrow Y$ of noetherian $k$-schemes, do we have an equivalence of:

1/ the cotangent complex $L_{X/Y}$ is concentrated in degree zero and is a flat module.

2/ $f$ is a regular morphism.

(2 implies 1 follows from Popescu's theorem).