Lemma 10.48.4. Let $k$ be a field. Let $R$ be a $k$-algebra. If $k$ is separably algebraically closed then $R$ is geometrically connected over $k$ if and only if the spectrum of $R$ is connected.

Proof. Immediate from the remark following Definition 10.48.3. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).