Lemma 101.19.1. In the situation above G_ x is a scheme if one of the following holds
\Delta : \mathcal{X} \to \mathcal{X} \times \mathcal{X} is quasi-separated
\Delta : \mathcal{X} \to \mathcal{X} \times \mathcal{X} is locally separated,
\mathcal{X} is quasi-DM,
\mathcal{I}_\mathcal {X} \to \mathcal{X} is quasi-separated,
\mathcal{I}_\mathcal {X} \to \mathcal{X} is locally separated, or
\mathcal{I}_\mathcal {X} \to \mathcal{X} is locally quasi-finite.
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