The Stacks project

Exercise 111.53.5. Chevalley's theorem and the Hilbert Nullstellensatz.

  1. Let $\mathfrak p \subset \mathbf{Z}[x_1, \ldots , x_ n]$ be a maximal ideal. What does Chevalley's theorem imply about $\mathfrak p \cap \mathbf{Z}$?

  2. In turn, what does the Hilbert Nullstellensatz imply about $\kappa (\mathfrak p)$?

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View Exercise 111.53.5 as pdf