For a $p$-divisible group $G$ over a smooth projective variety $X$ over $k$, where $k$ is a field finitely generated over a perfect field of characteristic $p$, we show that the formal group $R^i f_{ \fppf*} G$ is isogenous to a $p$-divisible group. The Dieudonn\'e crystal of its divisible part is canonically isomorphic to the slope-$[0,1]$ part of $R^i f_{ \crys*} \cM^{ cr}(G)$ in the category of $F$-isocrystals over $k$. This provides an answer to the rational form of a question of Artin--Mazur regarding the enlarged formal Brauer groups.
Categories: math.AG