Hi,

Let G be a smooth commutative $\mathbb{Z}_p$-group scheme of finite type and let $G_0$ be the $\mathbb{Q}_p$-fiber. We have an embedding $G(\mathbb{Z}_p)\subseteq G_0(\mathbb{Q}_p)$. My question is does every torsion point in $G_0(\mathbb{Q}_p)$ come from a torsion point in $G(\mathbb{Z}_p)$? I am mostly interested in the prime-to-p part of the torsion group. I think that the answer to this quesiton is yes, but I can't figure out how to prove it. Any ideas or references would be greatly appreciated.

Thanks in advance!

Neron modelmakes sense: it is a model over $\mathbb{Z}_p$ which satisfies the Neron mapping property. Unfortunately the Neron model of a group variety will not exist unless the component of the identity is semi-abelian. But Jason's comment still seems relevant: given that the answer in general is "no", this is one important case in which the answer is "yes". – Pete L. Clark Jul 8 '11 at 21:50