Lemma 33.25.1. Let k be a field. Let X be a scheme over k. Assume
X is locally of finite type over k,
\Omega _{X/k} is locally free, and
k has characteristic zero.
Then the structure morphism X \to \mathop{\mathrm{Spec}}(k) is smooth.
Lemma 33.25.1. Let k be a field. Let X be a scheme over k. Assume
X is locally of finite type over k,
\Omega _{X/k} is locally free, and
k has characteristic zero.
Then the structure morphism X \to \mathop{\mathrm{Spec}}(k) is smooth.
Proof. This follows from Algebra, Lemma 10.140.7. \square
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