The Stacks project

Example 89.11.12. The computation of Example 89.11.11 simplifies in the classical case. Namely, in this case the tangent space of the functor $F = \underline{S}|_{\mathcal{C}_\Lambda }$ is simply the relative cotangent space of $S$ over $\Lambda $, in a formula $TF = T_{S/\Lambda }$. In fact, this works more generally when the field extension $k/k'$ is separable. See Exercises, Exercise 110.35.2.