  We show that when $A$ is a reduced algebra over a characteristic zero field
$k$ and the module of K\"ahler differentials $\Omega_{A/k}=0$, then $A$ is
ind-\'etale, partially answering a question of Bhatt. As further applications
of this result, we deduce a rigidity property of Hochschild homology and
special instances of Weibel's conjecture and Vorst's conjecture without any
noetherian assumptions.
