Let $S=Spec A$ be the spectrum of an integrally closed, excellent and Noetherian ring. In his paper, David Mumford constructs an $S$-group scheme $G$. He shows that the torsion of $G_s$ is $p$-divisible for every prime $p$ and every $s\in S$ and concludes that $G_s$ is thus connected and without unipotent radical. I don't know how he comes to that conclusion. Is there something I don't know?

Let $S=Spec A$ be the spectrum of an integrally closed, excellent and Noetherian ring. In his paper, David Mumford constructs an $S$-group scheme $G$. He shows that the torsion of $G_s$ is $p$-divisible for every prime $p$ and every $s\in S$ and concludes that $G_s$ is thus connected and without unipotent radical. I do not know how he comes to that conclusion. Is there something I don't know?

Let $S=Spec A$ be the spectrum of an integrally closed, excellent and Noetherian ring. In his paper, David Mumford constructs an $S$-group scheme $G$. He shows that $G_s$ is $p$-divisible for every prime $p$ and every $s\in S$ and concludes that $G_s$ is thus connected and without unipotent radical. I don't know how he comes to that conclusion. Is there something I don't know?

Let $S=Spec A$ be the spectrum of an integrally closed, excellent and Noetherian ring. In his paper, David Mumford constructs an $S$-group scheme $G$. He shows that the torsion of $G_s$ is $p$-divisible for every prime $p$ and every $s\in S$ and concludes that $G_s$ is thus connected and without unipotent radical. I don't know how he comes to that conclusion. Is there something I don't know?