The Stacks project

Exercise 111.35.6. Let $k$ be a field. Consider the structure morphism $f : X = \mathbf{A}^1_ k \to \mathop{\mathrm{Spec}}(k) = S$.

  1. Let $x \in X$ be a closed point. What is the dimension of $T_{X/S, x}$?

  2. Let $\eta \in X$ be the generic point. What is the dimension of $T_{X/S, \eta }$?

  3. Consider now $X$ as a scheme over $\mathop{\mathrm{Spec}}(\mathbf{Z})$. What are the dimensions of $T_{X/\mathbf{Z}, x}$ and $T_{X/\mathbf{Z}, \eta }$?

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View Exercise 111.35.6 as pdf