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Exercise 111.34.1. Consider the morphism of schemes

\[ \pi : X = \mathop{\mathrm{Spec}}(\mathbf{C}[x, t, 1/xt]) \longrightarrow S = \mathop{\mathrm{Spec}}(\mathbf{C}[t]). \]

  1. Show there does not exist a morphism $\sigma : S \to X$ such that $\pi \circ \sigma = \text{id}_ S$.

  2. Show there does exist a nonempty open $U \subset S$ and a morphism $\sigma : U \to X$ such that $\pi \circ \sigma = \text{id}_ U$.

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View Exercise 111.34.1 as pdf