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Exercise 111.6.30. Compute $\mathop{\mathrm{Spec}}(k[x, y])$, where $k$ is algebraically closed. [Hint: use the morphism $\varphi : \mathop{\mathrm{Spec}}(k[x, y]) \to \mathop{\mathrm{Spec}}(k[x])$; if $\varphi ({\mathfrak p}) = (0)$ then localize with respect to $S = \{ f\in k[x] \mid f \not= 0\} $ and use result of lecture on localization and $\mathop{\mathrm{Spec}}$.] (Why do you think algebraic geometers call this affine 2-space?)

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View Exercise 111.6.30 as pdf