Rational points of finite etale group schemes over $\mathbb{Z}[1/N]$ Let $N$ be an integer and $G \to \mathrm{Spec}(\mathbf{Z}[1/N])$ be a finite étale group scheme. I read that, for every prime $p$ not diving $N$ we have :
$$
G(\overline{\mathbf{Q}}) = G(\overline{\mathbf{F}_p})
$$
Why is this true ?
 A: So, let's merely note that 
$$G(\overline{\mathbb{Q}})=G(R)=G_R(R)$$
where $R$ is the integral closure of $\mathbb{Z}[\frac{1}{N}]$ inside of $\overline{\mathbb{Q}}$. I claim that $G_R$ is constant. Indeed, by the standard equivalence between abelian LCC sheaves and finite étale group schemes, we know that $G$ is trivialized on some finite connected étale cover of $\mathrm{Spec}(\mathbb{Z}[\frac{1}{N}])$. But, evidently this is of the form $\mathrm{Spec}(S)$ where $S$ is the ring of integers in some finite extension of $\mathbb{Q}$ unramified outside of $N$. In particular, we see that $S\subseteq R$, and so the result follows.
But, note that we also have that
$$G(\overline{\mathbb{F}_p})=G_{\overline{\mathbb{F}_p}}(\overline{\mathbb{F}_p})=(G_R)_{\overline{\mathbb{F}_p}}(\overline{\mathbb{F}_p})$$
and thus we see that $G_{\overline{\mathbb{F}_p}}$ is constant. Thus, evidently the map 
$$G(\overline{\mathbb{Q}})=G_R(R)\to G(\overline{\mathbb{F_p}})$$
is, in fact, the identity once we identify both with the constant group scheme associated to $G$.
