F-isocrystals of Higher Direct Images of $p$-Divisible Groups

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 $R^i{f}_{\text{fppf}\ast }G$ is isogenous to a $p$-divisible group. The Dieudonné crystal of its divisible part is canonically isomorphic to the slope-$[0,1]$ part of $R^i{f}_{\text{crys}\ast }{\text{cM}}^{cr}(G)$ 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.