Let $S_0 \rightarrow S$ be a nilpotent thickening of schemes (no divided power provided) where $p$ is nilpotent, let $G$ be a $p$-divisble group over $S_0$, how to describe all liftings of $G$ to $S$ as $p$-divisible groups (using linear algebra data)?
I am curious about the existence in good cases which is trivial for etale ones. In general the original Grothendieck-Messing theory is not available (as no divided power structure is introduced), unless we're in some good cases like $\mathbb Z/p^n \rightarrow \mathbb Z/p^m$ ($p>2$).
