Let $S=Spec(R)$ where $R$ is a Henselian local ring with fraction field $K$. Let $G$ and $G'$ be finite, flat group schemes of odd order over $S$ with isomorphic generic fibers (over $Spec(K)$). Does this isomorphism extend to one over $S$?
When $R=\mathbb{Z}_p$, the answer is yes following Fontaine's discussion in his 1975 paper <i>'Groupes finis commutatifs sur les vecteurs de Witt'</i> (where he works over Witt vectors of a perfect field. Mazur uses this result to prove Theorem I.4 in his Eisenstein Ideal paper). What happens when $R$ is any general such ring?