Let $G$ be a quasi split reductive group over a scheme $S$. Let $B \subset G$ be the Borel subgroup. When does one has a short exact sequence of the following form
$$ 1 \rightarrow U \rightarrow B \rightarrow T \rightarrow 1$$
where $U$ is the unipotent radical of $B$ and $T$ a maximal torus. Generally for parabolic subgroups, the quotient by unipotent radical is a levi subgroup (which contains a maximal torus), but Borel subgroup being a minimal Parabolic subgroup, maybe one can say more.
When $S$ is a perfect field the above exact sequence does exist.I was wondering if it true for a general $S$ under some conditions i.e the quotient by unipotent radical is a torus or a group of multiplicative type.