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41.2 Conventions

In this chapter, frequently schemes will be assumed locally Noetherian and frequently rings will be assumed Noetherian. But in all the statements we will reiterate this when necessary, and make sure we list all the hypotheses! On the other hand, here are some general facts that we will use often and are useful to keep in mind:

  1. A ring homomorphism $A \to B$ of finite type with $A$ Noetherian is of finite presentation. See Algebra, Lemma 10.31.4.

  2. A morphism (locally) of finite type between locally Noetherian schemes is automatically (locally) of finite presentation. See Morphisms, Lemma 29.21.9.

  3. Add more like this here.

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