The Stacks project

Lemma 29.19.3. The following types of schemes are J-2.

  1. Any scheme locally of finite type over a field.

  2. Any scheme locally of finite type over a Noetherian complete local ring.

  3. Any scheme locally of finite type over $\mathbf{Z}$.

  4. Any scheme locally of finite type over a Noetherian local ring of dimension $1$.

  5. Any scheme locally of finite type over a Nagata ring of dimension $1$.

  6. Any scheme locally of finite type over a Dedekind ring of characteristic zero.

  7. And so on.

Proof. By Lemma 29.19.2 we only need to show that the rings mentioned above are J-2. For this see More on Algebra, Proposition 15.48.7. $\square$

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