Lemma 28.6.4. Examples of Noetherian Jacobson schemes.

If $(R, \mathfrak m)$ is a Noetherian local ring, then the punctured spectrum $\mathop{\mathrm{Spec}}(R) \setminus \{ \mathfrak m\} $ is a Jacobson scheme.

If $R$ is a Noetherian ring with Jacobson radical $\text{rad}(R)$ then $\mathop{\mathrm{Spec}}(R) \setminus V(\text{rad}(R))$ is a Jacobson scheme.

If $(R, I)$ is a Zariski pair (More on Algebra, Definition 15.10.1) with $R$ Noetherian, then $\mathop{\mathrm{Spec}}(R) \setminus V(I)$ is a Jacobson scheme.

## Comments (2)

Comment #2435 by Matthew Emerton on

Comment #2479 by Johan on