Ekedahl–Shepherd-Barron–Taylor conjecture on algebraic integrability of foliations

Let $X$ be a complex projective manifold, and let $F50A$ be a holomorphic foliation on $X$ with an integral model $(\mathscr X,\mathscr F)$ defined over a finitely generated $\mathbb Z$-algebra $R$. The reduction of this model at a closed point $\mathfrak p$ of residue characteristic $p$ is denoted by $\mathcal F_{\mathfrak p}$; it is $p$-closed when it is closed under the $p$-th power operation on vector fields. The foliation is algebraically integrable when all its leaves are algebraic.

Ekedahl–Shepherd-Barron–Taylor conjecture. The foliation $\mathcal F$ is algebraically integrable if and only if $\mathcal F_{\mathfrak p}$ is $p$-closed for every closed point $\mathfrak p$ in a non-empty Zariski open subset of $\operatorname{Spec}(R)$.

This conjecture proposes a criterion for algebraic integrability in terms of reductions in positive characteristic. The supplied text does not state whether it has been resolved.