Lemma 33.7.5. Let $k$ be a field. Let $A$ be a $k$-algebra. Then $X = \mathop{\mathrm{Spec}}(A)$ is geometrically connected over $k$ if and only if $A$ is geometrically connected over $k$ (see Algebra, Definition 10.48.3).

**Proof.**
Immediate from the definitions.
$\square$

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