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Results tagged with smoothness
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user 2757
10
votes
Example of a smooth morphism where you can't lift a map from a nilpotent thickening?
Let $Y=\operatorname{Spec} k$ and let $X=\mathbb{P}^1_k$, viewed as $\operatorname{Spec} k[t]$ glued to $\operatorname{Spec} k[t^{-1}]$.
Let $T = \operatorname{\bf Spec}(\mathcal{O}_X + \mathcal{O}_X( …
- 23.8k
24
votes
Accepted
Example of a smooth morphism where you can't lift a map from a nilpotent thickening?
By wicked smoothness, $x_0$ lifts to some $x_T \in X(T)$. …
- 23.8k