Lemma 39.4.4. Let $S$ be a scheme. Let $(G, m, e, i)$ be a group scheme over $S$.

A closed subscheme $H \subset G$ is a closed subgroup scheme if and only if $e : S \to G$, $m|_{H \times _ S H} : H \times _ S H \to G$, and $i|_ H : H \to G$ factor through $H$.

An open subscheme $H \subset G$ is an open subgroup scheme if and only if $e : S \to G$, $m|_{H \times _ S H} : H \times _ S H \to G$, and $i|_ H : H \to G$ factor through $H$.

## Comments (0)