Lemma 74.16.1. The property $\mathcal{P}(f)=$“$f$ is locally of finite presentation” is fppf local on the source.
74.16 Properties of morphisms local in the fppf topology on the source
Here are some properties of morphisms that are fppf local on the source.
Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.28.1 and Descent, Lemma 35.28.1. $\square$
Lemma 74.16.2. The property $\mathcal{P}(f)=$“$f$ is locally of finite type” is fppf local on the source.
Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.23.1 and Descent, Lemma 35.28.2. $\square$
Lemma 74.16.3. The property $\mathcal{P}(f)=$“$f$ is open” is fppf local on the source.
Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.6.2 and Descent, Lemma 35.28.3. $\square$
Lemma 74.16.4. The property $\mathcal{P}(f)=$“$f$ is universally open” is fppf local on the source.
Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.6.2 and Descent, Lemma 35.28.4. $\square$
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