Remark 39.8.5. Let $k$ be a field of characteristic $p > 0$. Let $\alpha \in k$ be an element which is not a $p$th power. The closed subgroup scheme
\[ G = V(x^ p + \alpha y^ p) \subset \mathbf{G}_{a, k}^2 \]
is reduced and irreducible but not smooth (not even normal).
Comments (0)