3 problems

Let $S$ be a scheme. A linear group scheme over $S$ is a group scheme $G\rightarrow S$ that, locally in the étale topology of $S$, embeds as a closed subgroup scheme of $GL(E)$ for…

Let $A$ be the base ring and let $G\in\operatorname{Gr}^{+}_{A}$ be a group scheme of additive type. Write $G=\operatorname{Spec}(B_G)$ and let $\operatorname{Prim}(B_G)$ denote th…

Let $A$ be the base ring, let $q$ be a power of the characteristic prime $p$, and let $G\in\mathbb{F}_{q}\text{-}\operatorname{Gr}^{+}_{A}$. Suppose that there is a closed embeddin…